id	sid	tid	token	lemma	pos
iajs-1020	1	1	ستويمفضاءات	ستويمفضاءات	NOUN
iajs-1020	1	2	جزئیة	جزئیة	NOUN
iajs-1020	1	3	في	في	ADP
iajs-1020	1	4	مجموعات	مجموعات	ADJ
iajs-1020	1	5	من	من	PRON
iajs-1020	1	6	gf(q)حول	gf(q)حول	PROPN
iajs-1020	1	7	حقل	حقل	PROPN
iajs-1020	1	8	كالوا	كالوا	NOUN
iajs-1020	1	9	pg(2,q)سقاطي	pg(2,q)سقاطي	PROPN
iajs-1020	1	10	ا	ا	PROPN
iajs-1020	1	11	میساء	میساء	ADJ
iajs-1020	1	12	جلیل	جلیل	ADJ
iajs-1020	1	13	محمد	محمد	PROPN
iajs-1020	1	14	جامعة	جامعة	NOUN
iajs-1020	1	15	بغداد	بغداد	PROPN
iajs-1020	1	16	،	،	PROPN
iajs-1020	1	17	ابن	ابن	PROPN
iajs-1020	1	18	الھیثم	الھیثم	PROPN
iajs-1020	1	19	-كلیة	-كلیة	PROPN
iajs-1020	1	20	التربیة	التربیة	NOUN
iajs-1020	1	21	،	،	NOUN
iajs-1020	1	22	قسم	قسم	PROPN
iajs-1020	1	23	الریاضیات	الریاضیات	PROPN
iajs-1020	1	24	خالصةال	خالصةال	PROPN
iajs-1020	1	25	حــول	حــول	PROPN
iajs-1020	1	26	pg(2,q)جزئیـة	pg(2,q)جزئیـة	ADP
iajs-1020	1	27	فــي	فــي	ADJ
iajs-1020	1	28	المسـتوي	المسـتوي	ADJ
iajs-1020	1	29	االسـقاطي	االسـقاطي	PROPN
iajs-1020	1	30	لفضـاءات	لفضـاءات	PROPN
iajs-1020	1	31	مجموعـات	مجموعـات	PROPN
iajs-1020	1	32	انـواع	انـواع	PROPN
iajs-1020	1	33	مــن	مــن	PROPN
iajs-1020	1	34	تتــم	تتــم	PROPN
iajs-1020	1	35	درسـفـي	درسـفـي	PROPN
iajs-1020	1	36	هـذا	هـذا	NOUN
iajs-1020	1	37	البحـث	البحـث	NOUN
iajs-1020	1	38	الـبعض	الـبعض	NOUN
iajs-1020	1	39	مـن	مـن	PROPN
iajs-1020	1	40	خـالل	خـالل	PROPN
iajs-1020	2	1	االمثلـة	االمثلـة	PROPN
iajs-1020	2	2	مـع	مـع	PROPN
iajs-1020	2	3	العالقـات	العالقـات	PROPN
iajs-1020	2	4	التـي	التـي	PROPN
iajs-1020	2	5	تـربط	تـربط	PROPN
iajs-1020	2	6	بـین	بـین	PROPN
iajs-1020	2	7	هـذه	هـذه	PROPN
iajs-1020	2	8	المجموعـات	المجموعـات	PROPN
iajs-1020	2	9	بعضـها	بعضـها	PROPN
iajs-1020	2	10	وبیـان	وبیـان	PROPN
iajs-1020	2	11	بعـض	بعـض	PROPN
iajs-1020	2	12	gf(q	gf(q	PROPN
iajs-1020	2	13	)	)	PUNCT
iajs-1020	2	14	.	.	PUNCT
iajs-1020	3	1	احقـل	احقـل	PROPN
iajs-1020	3	2	كـالو	كـالو	PROPN
iajs-1020	3	3	.والمبرهنات	.والمبرهنات	PROPN
iajs-1020	3	4	ihjpas	ihjpas	PROPN
iajs-1020	3	5	sets	set	NOUN
iajs-1020	3	6	of	of	ADP
iajs-1020	3	7	subspaces	subspace	NOUN
iajs-1020	3	8	of	of	ADP
iajs-1020	3	9	a	a	DET
iajs-1020	3	10	projective	projective	ADJ
iajs-1020	3	11	plane	plane	NOUN
iajs-1020	3	12	pg(2,q	pg(2,q	VERB
iajs-1020	3	13	)	)	PUNCT
iajs-1020	3	14	over	over	ADP
iajs-1020	3	15	galois	galois	PROPN
iajs-1020	3	16	field	field	NOUN
iajs-1020	3	17	gf(q	gf(q	NOUN
iajs-1020	3	18	)	)	PUNCT
iajs-1020	3	19	m.	m.	NOUN
iajs-1020	3	20	j.	j.	PROPN
iajs-1020	3	21	mahammad	mahammad	PROPN
iajs-1020	3	22	department	department	PROPN
iajs-1020	3	23	of	of	ADP
iajs-1020	3	24	mathematics	mathematics	PROPN
iajs-1020	3	25	,	,	PUNCT
iajs-1020	3	26	college	college	NOUN
iajs-1020	3	27	of	of	ADP
iajs-1020	3	28	education	education	PROPN
iajs-1020	3	29	ibn	ibn	PROPN
iajs-1020	3	30	-	-	PUNCT
iajs-1020	3	31	al	al	PROPN
iajs-1020	3	32	-	-	PUNCT
iajs-1020	3	33	haitham	haitham	PROPN
iajs-1020	3	34	,	,	PUNCT
iajs-1020	3	35	university	university	PROPN
iajs-1020	3	36	of	of	ADP
iajs-1020	3	37	baghdad	baghdad	PROPN
iajs-1020	3	38	abstract	abstract	ADV
iajs-1020	3	39	in	in	ADP
iajs-1020	3	40	this	this	DET
iajs-1020	3	41	thesis	thesis	NOUN
iajs-1020	3	42	,	,	PUNCT
iajs-1020	3	43	some	some	DET
iajs-1020	3	44	sets	set	NOUN
iajs-1020	3	45	of	of	ADP
iajs-1020	3	46	subspaces	subspace	NOUN
iajs-1020	3	47	of	of	ADP
iajs-1020	3	48	projective	projective	ADJ
iajs-1020	3	49	plane	plane	NOUN
iajs-1020	3	50	pg(2,q	pg(2,q	VERB
iajs-1020	3	51	)	)	PUNCT
iajs-1020	3	52	over	over	ADP
iajs-1020	3	53	galois	galois	PROPN
iajs-1020	3	54	field	field	NOUN
iajs-1020	3	55	gf(q	gf(q	NOUN
iajs-1020	3	56	)	)	PUNCT
iajs-1020	3	57	and	and	CCONJ
iajs-1020	3	58	the	the	DET
iajs-1020	3	59	relations	relation	NOUN
iajs-1020	3	60	between	between	ADP
iajs-1020	3	61	them	they	PRON
iajs-1020	3	62	by	by	ADP
iajs-1020	3	63	some	some	DET
iajs-1020	3	64	theorems	theorem	NOUN
iajs-1020	3	65	and	and	CCONJ
iajs-1020	3	66	examples	example	NOUN
iajs-1020	3	67	can	can	AUX
iajs-1020	3	68	be	be	AUX
iajs-1020	3	69	shown	show	VERB
iajs-1020	3	70	.	.	PUNCT
iajs-1020	4	1	1	1	X
iajs-1020	4	2	.	.	X
iajs-1020	4	3	introduction	introduction	NOUN
iajs-1020	4	4	a	a	DET
iajs-1020	4	5	recurring	recur	VERB
iajs-1020	4	6	them	they	PRON
iajs-1020	4	7	of	of	ADP
iajs-1020	4	8	this	this	DET
iajs-1020	4	9	work	work	NOUN
iajs-1020	4	10	is	be	AUX
iajs-1020	4	11	the	the	DET
iajs-1020	4	12	characterization	characterization	NOUN
iajs-1020	4	13	of	of	ADP
iajs-1020	4	14	algebraic	algebraic	ADJ
iajs-1020	4	15	varieties	variety	NOUN
iajs-1020	4	16	in	in	ADP
iajs-1020	4	17	pg(2,q	pg(2,q	NOUN
iajs-1020	4	18	)	)	PUNCT
iajs-1020	4	19	as	as	ADP
iajs-1020	4	20	finite	finite	ADJ
iajs-1020	4	21	sets	set	NOUN
iajs-1020	4	22	of	of	ADP
iajs-1020	4	23	points	point	NOUN
iajs-1020	4	24	with	with	ADP
iajs-1020	4	25	certain	certain	ADJ
iajs-1020	4	26	combinatorial	combinatorial	ADJ
iajs-1020	4	27	properties	property	NOUN
iajs-1020	4	28	of	of	ADP
iajs-1020	4	29	.	.	PUNCT
iajs-1020	5	1	this	this	DET
iajs-1020	5	2	work	work	NOUN
iajs-1020	5	3	.	.	PUNCT
iajs-1020	6	1	section	section	NOUN
iajs-1020	6	2	one	one	NUM
iajs-1020	6	3	which	which	PRON
iajs-1020	6	4	contains	contain	VERB
iajs-1020	6	5	some	some	DET
iajs-1020	6	6	definitions	definition	NOUN
iajs-1020	6	7	of	of	ADP
iajs-1020	6	8	nucleus	nucleus	ADJ
iajs-1020	6	9	point	point	NOUN
iajs-1020	6	10	,	,	PUNCT
iajs-1020	6	11	t	t	NOUN
iajs-1020	6	12	-	-	ADJ
iajs-1020	6	13	fold	fold	ADJ
iajs-1020	6	14	nucleus	nucleus	ADJ
iajs-1020	6	15	point	point	NOUN
iajs-1020	6	16	,	,	PUNCT
iajs-1020	6	17	blocking	block	VERB
iajs-1020	6	18	set	set	NOUN
iajs-1020	6	19	,	,	PUNCT
iajs-1020	6	20	t	t	NOUN
iajs-1020	6	21	-	-	PUNCT
iajs-1020	6	22	fold	fold	ADJ
iajs-1020	6	23	blocking	block	VERB
iajs-1020	6	24	set	set	NOUN
iajs-1020	6	25	,	,	PUNCT
iajs-1020	6	26	unital	unital	ADJ
iajs-1020	6	27	set	set	NOUN
iajs-1020	6	28	,	,	PUNCT
iajs-1020	6	29	(	(	PUNCT
iajs-1020	6	30	k	k	NOUN
iajs-1020	6	31	,	,	PUNCT
iajs-1020	6	32	n)-arc	n)-arc	NOUN
iajs-1020	6	33	,	,	PUNCT
iajs-1020	6	34	flag	flag	NOUN
iajs-1020	6	35	,	,	PUNCT
iajs-1020	6	36	strong	strong	ADJ
iajs-1020	6	37	representive	representive	ADJ
iajs-1020	6	38	system	system	NOUN
iajs-1020	6	39	and	and	CCONJ
iajs-1020	6	40	,	,	PUNCT
iajs-1020	6	41	the	the	DET
iajs-1020	6	42	set	set	NOUN
iajs-1020	6	43	of	of	ADP
iajs-1020	6	44	type	type	NOUN
iajs-1020	6	45	(	(	PUNCT
iajs-1020	6	46	0,1,2,q	0,1,2,q	NOUN
iajs-1020	6	47	+	+	CCONJ
iajs-1020	6	48	1	1	NUM
iajs-1020	6	49	)	)	PUNCT
iajs-1020	6	50	.	.	PUNCT
iajs-1020	7	1	section	section	NOUN
iajs-1020	7	2	two	two	NUM
iajs-1020	7	3	,	,	PUNCT
iajs-1020	7	4	contains	contain	VERB
iajs-1020	7	5	some	some	DET
iajs-1020	7	6	theorems	theorem	NOUN
iajs-1020	7	7	about	about	ADP
iajs-1020	7	8	these	these	DET
iajs-1020	7	9	subsets	subset	NOUN
iajs-1020	7	10	and	and	CCONJ
iajs-1020	7	11	the	the	DET
iajs-1020	7	12	relation	relation	NOUN
iajs-1020	7	13	between	between	ADP
iajs-1020	7	14	them	they	PRON
iajs-1020	7	15	and	and	CCONJ
iajs-1020	7	16	some	some	DET
iajs-1020	7	17	examples	example	NOUN
iajs-1020	7	18	which	which	PRON
iajs-1020	7	19	about	about	ADP
iajs-1020	7	20	some	some	PRON
iajs-1020	7	21	of	of	ADP
iajs-1020	7	22	these	these	DET
iajs-1020	7	23	subsets	subset	NOUN
iajs-1020	7	24	.	.	PUNCT
iajs-1020	8	1	2.1	2.1	NUM
iajs-1020	8	2	definition	definition	NOUN
iajs-1020	8	3	"	"	PUNCT
iajs-1020	8	4	projective	projective	ADJ
iajs-1020	8	5	plane	plane	NOUN
iajs-1020	8	6	"	"	PUNCT
iajs-1020	8	7	[	[	X
iajs-1020	8	8	2	2	NUM
iajs-1020	8	9	]	]	PUNCT
iajs-1020	8	10	a	a	DET
iajs-1020	8	11	projective	projective	ADJ
iajs-1020	8	12	plane	plane	NOUN
iajs-1020	8	13	pg(2,q	pg(2,q	VERB
iajs-1020	8	14	)	)	PUNCT
iajs-1020	8	15	over	over	ADP
iajs-1020	8	16	galois	galois	PROPN
iajs-1020	8	17	field	field	NOUN
iajs-1020	8	18	gf(q	gf(q	NOUN
iajs-1020	8	19	)	)	PUNCT
iajs-1020	8	20	is	be	AUX
iajs-1020	8	21	a	a	DET
iajs-1020	8	22	two	two	NUM
iajs-1020	8	23	-	-	PUNCT
iajs-1020	8	24	dimensional	dimensional	ADJ
iajs-1020	8	25	projective	projective	ADJ
iajs-1020	8	26	space	space	NOUN
iajs-1020	8	27	,	,	PUNCT
iajs-1020	8	28	which	which	PRON
iajs-1020	8	29	consists	consist	VERB
iajs-1020	8	30	of	of	ADP
iajs-1020	8	31	points	point	NOUN
iajs-1020	8	32	and	and	CCONJ
iajs-1020	8	33	lines	line	NOUN
iajs-1020	8	34	with	with	ADP
iajs-1020	8	35	relation	relation	NOUN
iajs-1020	8	36	between	between	ADP
iajs-1020	8	37	them	they	PRON
iajs-1020	8	38	,	,	PUNCT
iajs-1020	8	39	in	in	ADP
iajs-1020	8	40	pg(2,q	pg(2,q	NOUN
iajs-1020	8	41	)	)	PUNCT
iajs-1020	8	42	there	there	PRON
iajs-1020	8	43	are	be	VERB
iajs-1020	8	44	q	q	PROPN
iajs-1020	8	45	2	2	NUM
iajs-1020	8	46	+	+	CCONJ
iajs-1020	8	47	q	q	NOUN
iajs-1020	8	48	+	+	NUM
iajs-1020	8	49	1	1	NUM
iajs-1020	8	50	points	point	NOUN
iajs-1020	8	51	,	,	PUNCT
iajs-1020	8	52	and	and	CCONJ
iajs-1020	8	53	q	q	NOUN
iajs-1020	8	54	2	2	NUM
iajs-1020	8	55	+	+	CCONJ
iajs-1020	8	56	q	q	ADJ
iajs-1020	9	1	+	+	CCONJ
iajs-1020	9	2	1	1	NUM
iajs-1020	9	3	lines	line	NOUN
iajs-1020	9	4	,	,	PUNCT
iajs-1020	9	5	every	every	DET
iajs-1020	9	6	line	line	NOUN
iajs-1020	9	7	contains	contain	VERB
iajs-1020	9	8	1	1	NUM
iajs-1020	9	9	+	+	CCONJ
iajs-1020	9	10	q	q	ADJ
iajs-1020	9	11	points	point	NOUN
iajs-1020	9	12	and	and	CCONJ
iajs-1020	9	13	every	every	DET
iajs-1020	9	14	point	point	NOUN
iajs-1020	9	15	is	be	AUX
iajs-1020	9	16	on	on	ADP
iajs-1020	9	17	1	1	NUM
iajs-1020	9	18	+	+	NOUN
iajs-1020	9	19	q	q	ADJ
iajs-1020	9	20	lines	line	NOUN
iajs-1020	9	21	,	,	PUNCT
iajs-1020	9	22	any	any	DET
iajs-1020	9	23	point	point	NOUN
iajs-1020	9	24	in	in	ADP
iajs-1020	9	25	pg(2,q	pg(2,q	NOUN
iajs-1020	9	26	)	)	PUNCT
iajs-1020	9	27	has	have	VERB
iajs-1020	9	28	the	the	DET
iajs-1020	9	29	form	form	NOUN
iajs-1020	9	30	of	of	ADP
iajs-1020	9	31	a	a	DET
iajs-1020	9	32	triple	triple	ADJ
iajs-1020	9	33	(	(	PUNCT
iajs-1020	9	34	a1,a2,a3	a1,a2,a3	NOUN
iajs-1020	9	35	)	)	PUNCT
iajs-1020	9	36	where	where	SCONJ
iajs-1020	9	37	a1	a1	NOUN
iajs-1020	9	38	,	,	PUNCT
iajs-1020	9	39	a2	a2	PROPN
iajs-1020	9	40	,	,	PUNCT
iajs-1020	9	41	a3	a3	VERB
iajs-1020	9	42			PROPN
iajs-1020	9	43	gf(q	gf(q	NOUN
iajs-1020	9	44	)	)	PUNCT
iajs-1020	9	45	;	;	PUNCT
iajs-1020	9	46	such	such	ADJ
iajs-1020	9	47	that	that	SCONJ
iajs-1020	9	48	(	(	PUNCT
iajs-1020	9	49	a1,a2,a3	a1,a2,a3	PROPN
iajs-1020	9	50	)	)	PUNCT
iajs-1020	9	51			NOUN
iajs-1020	9	52	(	(	PUNCT
iajs-1020	9	53	0,0,0	0,0,0	NOUN
iajs-1020	9	54	)	)	PUNCT
iajs-1020	9	55	.	.	PUNCT
iajs-1020	10	1	two	two	NUM
iajs-1020	10	2	points	point	NOUN
iajs-1020	10	3	(	(	PUNCT
iajs-1020	10	4	a1,a2,a3	a1,a2,a3	NOUN
iajs-1020	10	5	)	)	PUNCT
iajs-1020	10	6	and	and	CCONJ
iajs-1020	10	7	(	(	PUNCT
iajs-1020	10	8	b1,b2,b3	b1,b2,b3	PROPN
iajs-1020	10	9	)	)	PUNCT
iajs-1020	10	10	represent	represent	VERB
iajs-1020	10	11	the	the	DET
iajs-1020	10	12	same	same	ADJ
iajs-1020	10	13	point	point	NOUN
iajs-1020	10	14	if	if	SCONJ
iajs-1020	10	15	there	there	PRON
iajs-1020	10	16	exists	exist	VERB
iajs-1020	10	17			ADJ
iajs-1020	10	18	gf(q)\{0	gf(q)\{0	NOUN
iajs-1020	10	19	}	}	PUNCT
iajs-1020	10	20	,	,	PUNCT
iajs-1020	10	21	such	such	ADJ
iajs-1020	10	22	that	that	SCONJ
iajs-1020	10	23	(	(	PUNCT
iajs-1020	10	24	b1,b2,b3	b1,b2,b3	PROPN
iajs-1020	10	25	)	)	PUNCT
iajs-1020	10	26	=	=	SYM
iajs-1020	10	27			X
iajs-1020	10	28	(	(	PUNCT
iajs-1020	10	29	a1,a2,a3	a1,a2,a3	NOUN
iajs-1020	10	30	)	)	PUNCT
iajs-1020	10	31	.	.	PUNCT
iajs-1020	11	1	similarly	similarly	ADV
iajs-1020	11	2	any	any	DET
iajs-1020	11	3	line	line	NOUN
iajs-1020	11	4	in	in	ADP
iajs-1020	11	5	pg(2,q	pg(2,q	NOUN
iajs-1020	11	6	)	)	PUNCT
iajs-1020	11	7	has	have	VERB
iajs-1020	11	8	the	the	DET
iajs-1020	11	9	form	form	NOUN
iajs-1020	11	10	of	of	ADP
iajs-1020	11	11	a	a	DET
iajs-1020	11	12	triple	triple	ADJ
iajs-1020	11	13	[	[	X
iajs-1020	11	14	a1,a2,a3	a1,a2,a3	ADP
iajs-1020	11	15	]	]	X
iajs-1020	11	16	,	,	PUNCT
iajs-1020	11	17	where	where	SCONJ
iajs-1020	11	18	a1,a2,a3	a1,a2,a3	ADP
iajs-1020	11	19			PROPN
iajs-1020	11	20	gf(q	gf(q	NOUN
iajs-1020	11	21	)	)	PUNCT
iajs-1020	11	22	;	;	PUNCT
iajs-1020	11	23	such	such	ADJ
iajs-1020	11	24	that	that	SCONJ
iajs-1020	12	1	[	[	X
iajs-1020	12	2	a1,a2,a3	a1,a2,a3	X
iajs-1020	12	3	]	]	X
iajs-1020	12	4	≠	≠	PROPN
iajs-1020	12	5	[	[	X
iajs-1020	12	6	0,0,0	0,0,0	NOUN
iajs-1020	12	7	]	]	X
iajs-1020	12	8	.	.	PUNCT
iajs-1020	13	1	two	two	NUM
iajs-1020	13	2	lines	line	NOUN
iajs-1020	14	1	[	[	X
iajs-1020	14	2	a1,a2,a3	a1,a2,a3	X
iajs-1020	14	3	]	]	PUNCT
iajs-1020	14	4	and	and	CCONJ
iajs-1020	14	5	[	[	X
iajs-1020	14	6	b1,b2,b3	b1,b2,b3	X
iajs-1020	14	7	]	]	PUNCT
iajs-1020	14	8	represent	represent	VERB
iajs-1020	14	9	the	the	DET
iajs-1020	14	10	same	same	ADJ
iajs-1020	14	11	line	line	NOUN
iajs-1020	14	12	if	if	SCONJ
iajs-1020	14	13	there	there	PRON
iajs-1020	14	14	exists	exist	VERB
iajs-1020	14	15			ADJ
iajs-1020	14	16	gf(q)\{0	gf(q)\{0	NOUN
iajs-1020	14	17	}	}	PUNCT
iajs-1020	14	18	,	,	PUNCT
iajs-1020	14	19	such	such	ADJ
iajs-1020	14	20	that	that	SCONJ
iajs-1020	14	21	[	[	X
iajs-1020	14	22	b1,b2,b3	b1,b2,b3	X
iajs-1020	14	23	]	]	X
iajs-1020	14	24	=	=	SYM
iajs-1020	14	25			X
iajs-1020	15	1	[	[	X
iajs-1020	15	2	a1,a2,a3	a1,a2,a3	ADP
iajs-1020	15	3	]	]	X
iajs-1020	15	4	.	.	PUNCT
iajs-1020	16	1	there	there	PRON
iajs-1020	16	2	exists	exist	VERB
iajs-1020	16	3	one	one	NUM
iajs-1020	16	4	point	point	NOUN
iajs-1020	16	5	of	of	ADP
iajs-1020	16	6	the	the	DET
iajs-1020	16	7	form	form	NOUN
iajs-1020	16	8	(	(	PUNCT
iajs-1020	16	9	1,0,0	1,0,0	NUM
iajs-1020	16	10	)	)	PUNCT
iajs-1020	16	11	.	.	PUNCT
iajs-1020	17	1	there	there	PRON
iajs-1020	17	2	exist	exist	VERB
iajs-1020	17	3	q	q	ADJ
iajs-1020	17	4	points	point	NOUN
iajs-1020	17	5	of	of	ADP
iajs-1020	17	6	the	the	DET
iajs-1020	17	7	form	form	NOUN
iajs-1020	17	8	(	(	PUNCT
iajs-1020	17	9	x,1,0	x,1,0	PROPN
iajs-1020	17	10	)	)	PUNCT
iajs-1020	17	11	.	.	PUNCT
iajs-1020	18	1	there	there	PRON
iajs-1020	18	2	exist	exist	VERB
iajs-1020	18	3	q	q	ADJ
iajs-1020	18	4	2	2	NUM
iajs-1020	18	5	points	point	NOUN
iajs-1020	18	6	of	of	ADP
iajs-1020	18	7	the	the	DET
iajs-1020	18	8	form	form	NOUN
iajs-1020	18	9	(	(	PUNCT
iajs-1020	18	10	x	x	X
iajs-1020	18	11	,	,	PUNCT
iajs-1020	18	12	y,1	y,1	PROPN
iajs-1020	18	13	)	)	PUNCT
iajs-1020	18	14	.	.	PUNCT
iajs-1020	19	1	a	a	DET
iajs-1020	19	2	point	point	NOUN
iajs-1020	19	3	p(x1,x2,x3	p(x1,x2,x3	NOUN
iajs-1020	19	4	)	)	PUNCT
iajs-1020	19	5	is	be	AUX
iajs-1020	19	6	incident	incident	NOUN
iajs-1020	19	7	with	with	ADP
iajs-1020	19	8	the	the	DET
iajs-1020	19	9	line	line	NOUN
iajs-1020	19	10	l[a1,a2,a3	l[a1,a2,a3	ADJ
iajs-1020	19	11	]	]	PUNCT
iajs-1020	20	1	if	if	SCONJ
iajs-1020	20	2	and	and	CCONJ
iajs-1020	20	3	only	only	ADV
iajs-1020	20	4	if	if	SCONJ
iajs-1020	20	5	a1x1	a1x1	NUM
iajs-1020	20	6	+	+	NOUN
iajs-1020	20	7	a2x2	a2x2	NOUN
iajs-1020	20	8	+	+	CCONJ
iajs-1020	20	9	a3x3	a3x3	X
iajs-1020	20	10	=	=	SYM
iajs-1020	20	11	0	0	NUM
iajs-1020	20	12	,	,	PUNCT
iajs-1020	20	13	i.e.	i.e.	X
iajs-1020	20	14	a	a	DET
iajs-1020	20	15	point	point	NOUN
iajs-1020	20	16	represented	represent	VERB
iajs-1020	20	17	by	by	ADP
iajs-1020	20	18	(	(	PUNCT
iajs-1020	20	19	x1,x2,x3	x1,x2,x3	PROPN
iajs-1020	20	20	)	)	PUNCT
iajs-1020	20	21	and	and	CCONJ
iajs-1020	20	22	the	the	DET
iajs-1020	20	23	line	line	NOUN
iajs-1020	20	24	represented	represent	VERB
iajs-1020	20	25	by	by	ADP
iajs-1020	20	26	1	1	NUM
iajs-1020	20	27	2	2	NUM
iajs-1020	20	28	3	3	NUM
iajs-1020	20	29	a	a	DET
iajs-1020	20	30	a	a	DET
iajs-1020	20	31	a	a	DET
iajs-1020	20	32			NOUN
iajs-1020	20	33			NOUN
iajs-1020	20	34			PROPN
iajs-1020	21	1			PROPN
iajs-1020	22	1			PROPN
iajs-1020	23	1			INTJ
iajs-1020	24	1			PROPN
iajs-1020	24	2			PROPN
iajs-1020	25	1			PROPN
iajs-1020	25	2			NOUN
iajs-1020	25	3	,	,	PUNCT
iajs-1020	25	4	then	then	ADV
iajs-1020	25	5	(	(	PUNCT
iajs-1020	25	6	x1,x2,x3	x1,x2,x3	PROPN
iajs-1020	25	7	)	)	PUNCT
iajs-1020	25	8	1	1	NUM
iajs-1020	25	9	2	2	NUM
iajs-1020	25	10	3	3	NUM
iajs-1020	25	11	a	a	DET
iajs-1020	25	12	a	a	DET
iajs-1020	25	13	a	a	DET
iajs-1020	25	14			NOUN
iajs-1020	26	1			NOUN
iajs-1020	26	2			PROPN
iajs-1020	27	1			PROPN
iajs-1020	28	1			PROPN
iajs-1020	29	1			INTJ
iajs-1020	30	1			PROPN
iajs-1020	30	2			PROPN
iajs-1020	31	1			ADJ
iajs-1020	31	2			PROPN
iajs-1020	31	3	=	=	SYM
iajs-1020	31	4	0	0	NUM
iajs-1020	31	5			ADP
iajs-1020	31	6	a1x1	a1x1	ADJ
iajs-1020	31	7	+	+	NOUN
iajs-1020	31	8	a2x2	a2x2	NOUN
iajs-1020	31	9	+	+	NUM
iajs-1020	31	10	a3x3=0	a3x3=0	NOUN
iajs-1020	31	11	.	.	PUNCT
iajs-1020	32	1	any	any	DET
iajs-1020	32	2	projective	projective	ADJ
iajs-1020	32	3	plane	plane	NOUN
iajs-1020	32	4	pg(2,q	pg(2,q	PRON
iajs-1020	32	5	)	)	PUNCT
iajs-1020	32	6	satisfies	satisfy	VERB
iajs-1020	32	7	the	the	DET
iajs-1020	32	8	following	following	ADJ
iajs-1020	32	9	axioms	axiom	NOUN
iajs-1020	32	10	:	:	PUNCT
iajs-1020	33	1	1	1	X
iajs-1020	33	2	.	.	X
iajs-1020	33	3	any	any	DET
iajs-1020	33	4	two	two	NUM
iajs-1020	33	5	distinct	distinct	ADJ
iajs-1020	33	6	lines	line	NOUN
iajs-1020	33	7	are	be	AUX
iajs-1020	33	8	intersected	intersect	VERB
iajs-1020	33	9	in	in	ADP
iajs-1020	33	10	a	a	DET
iajs-1020	33	11	unique	unique	ADJ
iajs-1020	33	12	point	point	NOUN
iajs-1020	33	13	.	.	PUNCT
iajs-1020	34	1	2	2	X
iajs-1020	34	2	.	.	X
iajs-1020	34	3	any	any	DET
iajs-1020	34	4	two	two	NUM
iajs-1020	34	5	distinct	distinct	ADJ
iajs-1020	34	6	points	point	NOUN
iajs-1020	34	7	are	be	AUX
iajs-1020	34	8	contained	contain	VERB
iajs-1020	34	9	in	in	ADP
iajs-1020	34	10	a	a	DET
iajs-1020	34	11	unique	unique	ADJ
iajs-1020	34	12	line	line	NOUN
iajs-1020	34	13	.	.	PUNCT
iajs-1020	35	1	3	3	X
iajs-1020	35	2	.	.	X
iajs-1020	35	3	there	there	PRON
iajs-1020	35	4	exist	exist	VERB
iajs-1020	35	5	at	at	ADV
iajs-1020	35	6	least	least	ADV
iajs-1020	35	7	four	four	NUM
iajs-1020	35	8	points	point	NOUN
iajs-1020	35	9	such	such	ADJ
iajs-1020	35	10	that	that	SCONJ
iajs-1020	35	11	no	no	DET
iajs-1020	35	12	three	three	NUM
iajs-1020	35	13	of	of	ADP
iajs-1020	35	14	them	they	PRON
iajs-1020	35	15	are	be	AUX
iajs-1020	35	16	collinear	collinear	ADJ
iajs-1020	35	17	.	.	PUNCT
iajs-1020	36	1	2.2	2.2	NUM
iajs-1020	36	2	definition	definition	NOUN
iajs-1020	36	3	"	"	PUNCT
iajs-1020	36	4	blocking	block	VERB
iajs-1020	36	5	s	s	VERB
iajs-1020	36	6	et"[2	et"[2	NOUN
iajs-1020	36	7	]	]	PUNCT
iajs-1020	36	8	a	a	DET
iajs-1020	36	9	blocking	block	VERB
iajs-1020	36	10	set	set	NOUN
iajs-1020	36	11	b	b	PROPN
iajs-1020	36	12	of	of	ADP
iajs-1020	36	13	pg(2,q	pg(2,q	NOUN
iajs-1020	36	14	)	)	PUNCT
iajs-1020	36	15	is	be	AUX
iajs-1020	36	16	a	a	DET
iajs-1020	36	17	set	set	NOUN
iajs-1020	36	18	of	of	ADP
iajs-1020	36	19	points	point	NOUN
iajs-1020	36	20	intersecting	intersect	VERB
iajs-1020	36	21	every	every	DET
iajs-1020	36	22	line	line	NOUN
iajs-1020	36	23	of	of	ADP
iajs-1020	36	24	pg(2,q	pg(2,q	NOUN
iajs-1020	36	25	)	)	PUNCT
iajs-1020	36	26	in	in	ADP
iajs-1020	36	27	at	at	ADV
iajs-1020	36	28	least	least	ADV
iajs-1020	36	29	one	one	NUM
iajs-1020	36	30	point	point	NOUN
iajs-1020	36	31	,	,	PUNCT
iajs-1020	36	32	so	so	CCONJ
iajs-1020	36	33	b	b	PROPN
iajs-1020	36	34	is	be	AUX
iajs-1020	36	35	blocking	block	VERB
iajs-1020	36	36	set	set	VERB
iajs-1020	36	37	if	if	SCONJ
iajs-1020	36	38	and	and	CCONJ
iajs-1020	36	39	only	only	ADV
iajs-1020	36	40	if	if	SCONJ
iajs-1020	36	41	pg(2,q)\b	pg(2,q)\b	NOUN
iajs-1020	36	42	is	be	AUX
iajs-1020	36	43	blocking	block	VERB
iajs-1020	36	44	set	set	NOUN
iajs-1020	36	45	.	.	PUNCT
iajs-1020	37	1	ihjpas	ihjpa	VERB
iajs-1020	37	2	2.3	2.3	NUM
iajs-1020	37	3	definition	definition	NOUN
iajs-1020	37	4	"	"	PUNCT
iajs-1020	37	5	minimal	minimal	ADJ
iajs-1020	37	6	blocking	blocking	NOUN
iajs-1020	37	7	s	s	PART
iajs-1020	37	8	et	et	NOUN
iajs-1020	37	9	"	"	PUNCT
iajs-1020	38	1	[	[	X
iajs-1020	38	2	2	2	X
iajs-1020	38	3	]	]	PUNCT
iajs-1020	38	4	a	a	DET
iajs-1020	38	5	blocking	blocking	NOUN
iajs-1020	38	6	set	set	NOUN
iajs-1020	38	7	b	b	NUM
iajs-1020	38	8	is	be	AUX
iajs-1020	38	9	called	call	VERB
iajs-1020	38	10	minimal	minimal	ADJ
iajs-1020	38	11	in	in	ADP
iajs-1020	38	12	pg(2,q	pg(2,q	NOUN
iajs-1020	38	13	)	)	PUNCT
iajs-1020	38	14	when	when	SCONJ
iajs-1020	38	15	no	no	DET
iajs-1020	38	16	proper	proper	ADJ
iajs-1020	38	17	subset	subset	NOUN
iajs-1020	38	18	of	of	ADP
iajs-1020	38	19	it	it	PRON
iajs-1020	38	20	is	be	AUX
iajs-1020	38	21	still	still	ADV
iajs-1020	38	22	a	a	DET
iajs-1020	38	23	blocking	blocking	NOUN
iajs-1020	38	24	set	set	NOUN
iajs-1020	38	25	such	such	ADJ
iajs-1020	38	26	that	that	SCONJ
iajs-1020	38	27	,	,	PUNCT
iajs-1020	38	28			NOUN
iajs-1020	38	29	p	p	PROPN
iajs-1020	38	30			PROPN
iajs-1020	38	31	b	b	NOUN
iajs-1020	38	32	,	,	PUNCT
iajs-1020	38	33	b\{p	b\{p	NOUN
iajs-1020	38	34	}	}	PUNCT
iajs-1020	38	35	is	be	AUX
iajs-1020	38	36	not	not	PART
iajs-1020	38	37	a	a	DET
iajs-1020	38	38	blocking	blocking	NOUN
iajs-1020	38	39	set	set	NOUN
iajs-1020	38	40	.	.	PUNCT
iajs-1020	39	1	2.4	2.4	NUM
iajs-1020	39	2	definition	definition	NOUN
iajs-1020	39	3	"	"	PUNCT
iajs-1020	39	4	nuclei	nucleus	NOUN
iajs-1020	39	5	set"[2	set"[2	ADV
iajs-1020	39	6	]	]	X
iajs-1020	39	7	let	let	VERB
iajs-1020	39	8	s	s	PRON
iajs-1020	39	9	be	be	AUX
iajs-1020	39	10	a	a	DET
iajs-1020	39	11	set	set	NOUN
iajs-1020	39	12	in	in	ADP
iajs-1020	39	13	pg(2,q	pg(2,q	NOUN
iajs-1020	39	14	)	)	PUNCT
iajs-1020	39	15	,	,	PUNCT
iajs-1020	39	16	let	let	VERB
iajs-1020	39	17	p	p	PRON
iajs-1020	39	18	be	be	AUX
iajs-1020	39	19	a	a	DET
iajs-1020	39	20	point	point	NOUN
iajs-1020	39	21	in	in	ADP
iajs-1020	39	22	pg(2,q	pg(2,q	NOUN
iajs-1020	39	23	)	)	PUNCT
iajs-1020	39	24	and	and	CCONJ
iajs-1020	39	25	p	p	X
iajs-1020	39	26			NUM
iajs-1020	39	27	s	s	PROPN
iajs-1020	39	28	,	,	PUNCT
iajs-1020	39	29	p	p	PRON
iajs-1020	39	30	is	be	AUX
iajs-1020	39	31	called	call	VERB
iajs-1020	39	32	nucleus	nucleus	ADJ
iajs-1020	39	33	point	point	NOUN
iajs-1020	39	34	of	of	ADP
iajs-1020	39	35	a	a	DET
iajs-1020	39	36	set	set	NOUN
iajs-1020	39	37	s	s	X
iajs-1020	39	38	if	if	SCONJ
iajs-1020	39	39	every	every	DET
iajs-1020	39	40	line	line	NOUN
iajs-1020	39	41	in	in	ADP
iajs-1020	39	42	pg(2,q	pg(2,q	NOUN
iajs-1020	39	43	)	)	PUNCT
iajs-1020	39	44	through	through	ADP
iajs-1020	39	45	p	p	NOUN
iajs-1020	39	46	intersects	intersect	NOUN
iajs-1020	39	47	s	s	VERB
iajs-1020	39	48	exactly	exactly	ADV
iajs-1020	39	49	one	one	NUM
iajs-1020	39	50	,	,	PUNCT
iajs-1020	39	51	the	the	DET
iajs-1020	39	52	set	set	NOUN
iajs-1020	39	53	of	of	ADP
iajs-1020	39	54	nucleus	nucleus	ADJ
iajs-1020	39	55	points	point	NOUN
iajs-1020	39	56	of	of	ADP
iajs-1020	39	57	s	s	AUX
iajs-1020	39	58	called	call	VERB
iajs-1020	39	59	nuclei	nucleus	NOUN
iajs-1020	39	60	set	set	VERB
iajs-1020	39	61	and	and	CCONJ
iajs-1020	39	62	denoted	denote	VERB
iajs-1020	39	63	by	by	ADP
iajs-1020	39	64	n(s	n(s	PROPN
iajs-1020	39	65	)	)	PUNCT
iajs-1020	39	66	.	.	PUNCT
iajs-1020	40	1	by	by	ADP
iajs-1020	40	2	the	the	DET
iajs-1020	40	3	following	following	ADJ
iajs-1020	40	4	example	example	NOUN
iajs-1020	40	5	we	we	PRON
iajs-1020	40	6	explain	explain	VERB
iajs-1020	40	7	the	the	DET
iajs-1020	40	8	definition	definition	NOUN
iajs-1020	40	9	:	:	PUNCT
iajs-1020	40	10	in	in	ADP
iajs-1020	40	11	a	a	DET
iajs-1020	40	12	projective	projective	ADJ
iajs-1020	40	13	plane	plane	NOUN
iajs-1020	40	14	pg(2,4	pg(2,4	NOUN
iajs-1020	40	15	)	)	PUNCT
iajs-1020	40	16	,	,	PUNCT
iajs-1020	40	17	let	let	VERB
iajs-1020	40	18	s	s	PRON
iajs-1020	40	19	=	=	PUNCT
iajs-1020	40	20	{	{	PUNCT
iajs-1020	40	21	5,6,8,9,10,12,13,14,15,16,17,18,21	5,6,8,9,10,12,13,14,15,16,17,18,21	NUM
iajs-1020	40	22	}	}	PUNCT
iajs-1020	40	23	and	and	CCONJ
iajs-1020	40	24	let	let	VERB
iajs-1020	40	25	n(s	n(s	PRON
iajs-1020	40	26	)	)	PUNCT
iajs-1020	40	27	=	=	PRON
iajs-1020	40	28	{	{	PUNCT
iajs-1020	40	29	1,2,3,4	1,2,3,4	NUM
iajs-1020	40	30	}	}	PUNCT
iajs-1020	40	31	then	then	ADV
iajs-1020	40	32			NOUN
iajs-1020	40	33	p	p	PROPN
iajs-1020	40	34			PROPN
iajs-1020	40	35	n(s	n(s	PROPN
iajs-1020	40	36	)	)	PUNCT
iajs-1020	40	37	;	;	PUNCT
iajs-1020	40	38	p	p	PRON
iajs-1020	40	39	is	be	AUX
iajs-1020	40	40	nucleus	nucleus	ADJ
iajs-1020	40	41	point	point	NOUN
iajs-1020	40	42	since	since	SCONJ
iajs-1020	40	43	:	:	PUNCT
iajs-1020	40	44	through	through	ADP
iajs-1020	40	45	point	point	NOUN
iajs-1020	40	46	1	1	NUM
iajs-1020	40	47	,	,	PUNCT
iajs-1020	40	48	there	there	PRON
iajs-1020	40	49	are	be	VERB
iajs-1020	40	50	5	5	NUM
iajs-1020	40	51	lines	line	NOUN
iajs-1020	40	52	which	which	PRON
iajs-1020	40	53	are	be	AUX
iajs-1020	40	54	[	[	X
iajs-1020	40	55	1	1	NUM
iajs-1020	40	56	0	0	NUM
iajs-1020	40	57	0	0	NUM
iajs-1020	40	58	]	]	PUNCT
iajs-1020	40	59	,	,	PUNCT
iajs-1020	41	1	[	[	X
iajs-1020	41	2	0	0	NUM
iajs-1020	41	3	0	0	NUM
iajs-1020	41	4	1],[2	1],[2	NUM
iajs-1020	41	5	0	0	NUM
iajs-1020	41	6	1	1	NUM
iajs-1020	41	7	]	]	PUNCT
iajs-1020	41	8	,	,	PUNCT
iajs-1020	41	9	[	[	X
iajs-1020	41	10	0	0	NUM
iajs-1020	41	11	3	3	NUM
iajs-1020	41	12	1],[3	1],[3	NUM
iajs-1020	41	13	3	3	NUM
iajs-1020	41	14	1	1	NUM
iajs-1020	41	15	]	]	PUNCT
iajs-1020	41	16	such	such	ADJ
iajs-1020	41	17	that	that	SCONJ
iajs-1020	41	18	each	each	DET
iajs-1020	41	19	one	one	NUM
iajs-1020	41	20	of	of	ADP
iajs-1020	41	21	them	they	PRON
iajs-1020	41	22	intersects	intersect	VERB
iajs-1020	41	23	s	s	NOUN
iajs-1020	41	24	in	in	ADP
iajs-1020	41	25	one	one	NUM
iajs-1020	41	26	point	point	NOUN
iajs-1020	41	27	which	which	PRON
iajs-1020	41	28	are	be	AUX
iajs-1020	41	29	{	{	PUNCT
iajs-1020	41	30	5,9,10,14,18	5,9,10,14,18	NOUN
iajs-1020	41	31	}	}	PUNCT
iajs-1020	41	32	,	,	PUNCT
iajs-1020	41	33	respectively	respectively	ADV
iajs-1020	41	34	.	.	PUNCT
iajs-1020	42	1	similarly	similarly	ADV
iajs-1020	42	2	for	for	ADP
iajs-1020	42	3	the	the	DET
iajs-1020	42	4	other	other	ADJ
iajs-1020	42	5	points	point	NOUN
iajs-1020	42	6	{	{	PUNCT
iajs-1020	42	7	2,3,4	2,3,4	NUM
iajs-1020	42	8	}	}	PUNCT
iajs-1020	42	9	.	.	PUNCT
iajs-1020	43	1	2.5	2.5	NUM
iajs-1020	43	2	definition	definition	NOUN
iajs-1020	43	3	"	"	PUNCT
iajs-1020	43	4	t	t	NOUN
iajs-1020	43	5	-	-	ADJ
iajs-1020	43	6	fold	fold	ADJ
iajs-1020	43	7	nucleus	nucleus	PROPN
iajs-1020	43	8	point"[4	point"[4	PROPN
iajs-1020	43	9	]	]	PUNCT
iajs-1020	43	10	a	a	DET
iajs-1020	43	11	point	point	NOUN
iajs-1020	43	12	p	p	PRON
iajs-1020	43	13			NOUN
iajs-1020	43	14	pg(2,q	pg(2,q	VERB
iajs-1020	43	15	)	)	PUNCT
iajs-1020	43	16	is	be	AUX
iajs-1020	43	17	a	a	DET
iajs-1020	43	18	t	t	NOUN
iajs-1020	43	19	-	-	ADJ
iajs-1020	43	20	fold	fold	ADJ
iajs-1020	43	21	nucleus	nucleus	ADJ
iajs-1020	43	22	point	point	NOUN
iajs-1020	43	23	of	of	ADP
iajs-1020	43	24	a	a	DET
iajs-1020	43	25	set	set	NOUN
iajs-1020	43	26	s	s	PART
iajs-1020	43	27			NOUN
iajs-1020	43	28	pg(2,q	pg(2,q	PRON
iajs-1020	43	29	)	)	PUNCT
iajs-1020	43	30	if	if	SCONJ
iajs-1020	43	31	p	p	PROPN
iajs-1020	43	32			NOUN
iajs-1020	43	33	s	s	X
iajs-1020	43	34	and	and	CCONJ
iajs-1020	43	35	every	every	DET
iajs-1020	43	36	line	line	NOUN
iajs-1020	43	37	through	through	ADP
iajs-1020	43	38	p	p	PROPN
iajs-1020	43	39	meets	meet	VERB
iajs-1020	43	40	s	s	PRON
iajs-1020	43	41	at	at	ADV
iajs-1020	43	42	least	least	ADJ
iajs-1020	43	43	t	t	NOUN
iajs-1020	43	44	points	point	NOUN
iajs-1020	43	45	of	of	ADP
iajs-1020	43	46	s.	s.	PROPN
iajs-1020	43	47	2.6	2.6	NUM
iajs-1020	43	48	definition	definition	NOUN
iajs-1020	43	49	"	"	PUNCT
iajs-1020	43	50	unital	unital	ADJ
iajs-1020	43	51	set	set	NOUN
iajs-1020	43	52	"	"	PUNCT
iajs-1020	44	1	[	[	X
iajs-1020	44	2	1	1	X
iajs-1020	44	3	]	]	PUNCT
iajs-1020	44	4	a	a	DET
iajs-1020	44	5	unital	unital	ADJ
iajs-1020	44	6	set	set	NOUN
iajs-1020	44	7	pg(2,q	pg(2,q	PROPN
iajs-1020	44	8	)	)	PUNCT
iajs-1020	44	9	of	of	ADP
iajs-1020	44	10	a	a	DET
iajs-1020	44	11	square	square	ADJ
iajs-1020	44	12	order	order	NOUN
iajs-1020	44	13	q	q	NOUN
iajs-1020	44	14	is	be	AUX
iajs-1020	44	15	a	a	DET
iajs-1020	44	16	set	set	ADJ
iajs-1020	44	17	u	u	NOUN
iajs-1020	44	18	of	of	ADP
iajs-1020	44	19	(	(	PUNCT
iajs-1020	44	20	q	q	X
iajs-1020	44	21	q	q	X
iajs-1020	44	22	+1	+1	NOUN
iajs-1020	44	23	)	)	PUNCT
iajs-1020	44	24	points	point	NOUN
iajs-1020	44	25	such	such	ADJ
iajs-1020	44	26	that	that	SCONJ
iajs-1020	44	27	each	each	DET
iajs-1020	44	28	line	line	NOUN
iajs-1020	44	29	in	in	ADP
iajs-1020	44	30	pg(2,q	pg(2,q	NOUN
iajs-1020	44	31	)	)	PUNCT
iajs-1020	44	32	meets	meet	VERB
iajs-1020	44	33	u	u	NOUN
iajs-1020	44	34	either	either	DET
iajs-1020	44	35	one	one	NUM
iajs-1020	44	36	or	or	CCONJ
iajs-1020	44	37	q	q	NOUN
iajs-1020	44	38	+1	+1	ADJ
iajs-1020	44	39	points	point	NOUN
iajs-1020	44	40	,	,	PUNCT
iajs-1020	44	41	i.e.	i.e.	X
iajs-1020	44	42	,	,	PUNCT
iajs-1020	44	43	every	every	DET
iajs-1020	44	44	line	line	NOUN
iajs-1020	44	45	in	in	ADP
iajs-1020	44	46	pg(2,q	pg(2,q	NOUN
iajs-1020	44	47	)	)	PUNCT
iajs-1020	44	48	is	be	AUX
iajs-1020	44	49	a	a	DET
iajs-1020	44	50	tangent	tangent	NOUN
iajs-1020	44	51	or	or	CCONJ
iajs-1020	44	52	a	a	DET
iajs-1020	44	53	secant	secant	NOUN
iajs-1020	44	54	of	of	ADP
iajs-1020	44	55	u	u	PRON
iajs-1020	44	56	if	if	SCONJ
iajs-1020	44	57	contain	contain	VERB
iajs-1020	44	58	(	(	PUNCT
iajs-1020	44	59	1	1	NUM
iajs-1020	44	60	)	)	PUNCT
iajs-1020	44	61	point	point	NOUN
iajs-1020	44	62	or	or	CCONJ
iajs-1020	44	63	(	(	PUNCT
iajs-1020	44	64	q	q	PROPN
iajs-1020	44	65	+1	+1	ADJ
iajs-1020	44	66	)	)	PUNCT
iajs-1020	44	67	points	point	NOUN
iajs-1020	44	68	of	of	ADP
iajs-1020	44	69	line	line	NOUN
iajs-1020	44	70	.	.	PUNCT
iajs-1020	45	1	by	by	ADP
iajs-1020	45	2	the	the	DET
iajs-1020	45	3	following	following	ADJ
iajs-1020	45	4	example	example	NOUN
iajs-1020	45	5	we	we	PRON
iajs-1020	45	6	explain	explain	VERB
iajs-1020	45	7	the	the	DET
iajs-1020	45	8	definition	definition	NOUN
iajs-1020	45	9	:	:	PUNCT
iajs-1020	45	10	let	let	VERB
iajs-1020	45	11	u	u	PRON
iajs-1020	45	12	=	=	PUNCT
iajs-1020	45	13	{	{	PUNCT
iajs-1020	45	14	1,6,7,10,11,16,17,18,19	1,6,7,10,11,16,17,18,19	PROPN
iajs-1020	45	15	}	}	PUNCT
iajs-1020	45	16	be	be	AUX
iajs-1020	45	17	a	a	DET
iajs-1020	45	18	set	set	NOUN
iajs-1020	45	19	in	in	ADP
iajs-1020	45	20	pg(2,4	pg(2,4	NOUN
iajs-1020	45	21	)	)	PUNCT
iajs-1020	45	22	and	and	CCONJ
iajs-1020	45	23	u	u	NOUN
iajs-1020	45	24	contains	contain	VERB
iajs-1020	45	25	9	9	NUM
iajs-1020	45	26	points	point	NOUN
iajs-1020	45	27	.	.	PUNCT
iajs-1020	46	1	u	u	NOUN
iajs-1020	46	2	is	be	AUX
iajs-1020	46	3	a	a	DET
iajs-1020	46	4	unital	unital	ADJ
iajs-1020	46	5	set	set	NOUN
iajs-1020	46	6	since	since	SCONJ
iajs-1020	46	7	:	:	PUNCT
iajs-1020	46	8	u	u	NOUN
iajs-1020	46	9	contains	contain	VERB
iajs-1020	46	10	4	4	NUM
iajs-1020	46	11	4	4	NUM
iajs-1020	46	12	+1	+1	NOUN
iajs-1020	46	13	=	=	SYM
iajs-1020	46	14	9	9	NUM
iajs-1020	46	15	points	point	NOUN
iajs-1020	46	16	and	and	CCONJ
iajs-1020	46	17	every	every	PRON
iajs-1020	46	18	and	and	CCONJ
iajs-1020	46	19	line	line	NOUN
iajs-1020	46	20	in	in	ADP
iajs-1020	46	21	pg(2,4	pg(2,4	NOUN
iajs-1020	46	22	)	)	PUNCT
iajs-1020	46	23	meets	meet	VERB
iajs-1020	46	24	u	u	NOUN
iajs-1020	46	25	in	in	ADP
iajs-1020	46	26	1	1	NUM
iajs-1020	46	27	or	or	CCONJ
iajs-1020	46	28	3	3	NUM
iajs-1020	46	29	points	point	NOUN
iajs-1020	46	30	,	,	PUNCT
iajs-1020	46	31	as	as	SCONJ
iajs-1020	46	32	shown	show	VERB
iajs-1020	46	33	in	in	ADP
iajs-1020	46	34	the	the	DET
iajs-1020	46	35	table	table	NOUN
iajs-1020	46	36	(	(	PUNCT
iajs-1020	46	37	1,2	1,2	NUM
iajs-1020	46	38	)	)	PUNCT
iajs-1020	46	39	.	.	PUNCT
iajs-1020	47	1	2.7	2.7	NUM
iajs-1020	47	2	definition	definition	NOUN
iajs-1020	47	3	"	"	PUNCT
iajs-1020	47	4	(	(	PUNCT
iajs-1020	47	5	0,1,2,q	0,1,2,q	NOUN
iajs-1020	47	6	+	+	CCONJ
iajs-1020	47	7	1)-set"[1	1)-set"[1	NUM
iajs-1020	47	8	]	]	X
iajs-1020	47	9	a	a	DET
iajs-1020	47	10	set	set	NOUN
iajs-1020	47	11	of	of	ADP
iajs-1020	47	12	points	point	NOUN
iajs-1020	47	13	in	in	ADP
iajs-1020	47	14	pg(2,q	pg(2,q	NOUN
iajs-1020	47	15	)	)	PUNCT
iajs-1020	47	16	is	be	AUX
iajs-1020	47	17	called	call	VERB
iajs-1020	47	18	of	of	ADP
iajs-1020	47	19	type	type	NOUN
iajs-1020	47	20	(	(	PUNCT
iajs-1020	47	21	0,1,2,q	0,1,2,q	NOUN
iajs-1020	47	22	+	+	CCONJ
iajs-1020	47	23	1	1	X
iajs-1020	47	24	)	)	PUNCT
iajs-1020	47	25	if	if	SCONJ
iajs-1020	47	26	every	every	DET
iajs-1020	47	27	line	line	NOUN
iajs-1020	47	28	in	in	ADP
iajs-1020	47	29	pg(2,q	pg(2,q	NOUN
iajs-1020	47	30	)	)	PUNCT
iajs-1020	47	31	meets	meet	VERB
iajs-1020	47	32	the	the	DET
iajs-1020	47	33	set	set	NOUN
iajs-1020	47	34	in	in	ADP
iajs-1020	47	35	0,1,2	0,1,2	NUM
iajs-1020	47	36	or	or	CCONJ
iajs-1020	47	37	q	q	NOUN
iajs-1020	48	1	+	+	CCONJ
iajs-1020	48	2	1	1	NUM
iajs-1020	48	3	points	point	NOUN
iajs-1020	48	4	.	.	PUNCT
iajs-1020	49	1	2.8	2.8	NUM
iajs-1020	49	2	definition	definition	NOUN
iajs-1020	49	3	"	"	PUNCT
iajs-1020	49	4	n	n	CCONJ
iajs-1020	49	5	-	-	PUNCT
iajs-1020	49	6	secant"[2	secant"[2	NOUN
iajs-1020	49	7	]	]	X
iajs-1020	49	8	a	a	DET
iajs-1020	49	9	line	line	NOUN
iajs-1020	49	10	l	l	NOUN
iajs-1020	49	11	in	in	ADP
iajs-1020	49	12	pg(2,q	pg(2,q	NOUN
iajs-1020	49	13	)	)	PUNCT
iajs-1020	49	14	is	be	AUX
iajs-1020	49	15	an	an	DET
iajs-1020	49	16	i	i	NOUN
iajs-1020	49	17	-	-	PUNCT
iajs-1020	49	18	secant	secant	NOUN
iajs-1020	49	19	of	of	ADP
iajs-1020	49	20	a	a	DET
iajs-1020	49	21	(	(	PUNCT
iajs-1020	49	22	k	k	NOUN
iajs-1020	49	23	,	,	PUNCT
iajs-1020	49	24	n)-arc	n)-arc	X
iajs-1020	49	25	k	k	PROPN
iajs-1020	50	1	if	if	SCONJ
iajs-1020	50	2	:	:	PUNCT
iajs-1020	50	3			NUM
iajs-1020	50	4	k∩	k∩	PROPN
iajs-1020	50	5	l	l	PROPN
iajs-1020	50	6	=	=	PROPN
iajs-1020	50	7	i	i	PRON
iajs-1020	50	8	,	,	PUNCT
iajs-1020	50	9	i=0,1,2,	i=0,1,2,	VERB
iajs-1020	50	10	......	......	PUNCT
iajs-1020	50	11	,n	,n	NOUN
iajs-1020	50	12	.	.	PUNCT
iajs-1020	51	1	2.9	2.9	NUM
iajs-1020	51	2	definition	definition	NOUN
iajs-1020	51	3	"	"	PUNCT
iajs-1020	51	4	(	(	PUNCT
iajs-1020	51	5	k	k	NOUN
iajs-1020	51	6	,	,	PUNCT
iajs-1020	51	7	n)-arc	n)-arc	NOUN
iajs-1020	51	8	"	"	PUNCT
iajs-1020	52	1	[	[	X
iajs-1020	52	2	2	2	X
iajs-1020	52	3	]	]	X
iajs-1020	52	4	a	a	DET
iajs-1020	52	5	(	(	PUNCT
iajs-1020	52	6	k	k	NOUN
iajs-1020	52	7	,	,	PUNCT
iajs-1020	52	8	n)-arc	n)-arc	ADV
iajs-1020	52	9	in	in	ADP
iajs-1020	52	10	pg(2,q	pg(2,q	NOUN
iajs-1020	52	11	)	)	PUNCT
iajs-1020	52	12	is	be	AUX
iajs-1020	52	13	a	a	DET
iajs-1020	52	14	set	set	NOUN
iajs-1020	52	15	s	s	X
iajs-1020	52	16	of	of	ADP
iajs-1020	52	17	k	k	PROPN
iajs-1020	52	18	points	point	NOUN
iajs-1020	52	19	with	with	ADP
iajs-1020	52	20	property	property	NOUN
iajs-1020	52	21	that	that	PRON
iajs-1020	52	22	every	every	DET
iajs-1020	52	23	line	line	NOUN
iajs-1020	52	24	i	i	PRON
iajs-1020	52	25	contains	contain	VERB
iajs-1020	52	26	at	at	ADP
iajs-1020	52	27	most	most	ADJ
iajs-1020	52	28	n	n	NUM
iajs-1020	52	29	points	point	NOUN
iajs-1020	52	30	of	of	ADP
iajs-1020	52	31	s	s	PROPN
iajs-1020	52	32	,	,	PUNCT
iajs-1020	52	33	a	a	DET
iajs-1020	52	34	(	(	PUNCT
iajs-1020	52	35	k	k	NOUN
iajs-1020	52	36	,	,	PUNCT
iajs-1020	52	37	n)-arc	n)-arc	X
iajs-1020	52	38	s	s	PART
iajs-1020	52	39	is	be	AUX
iajs-1020	52	40	called	call	VERB
iajs-1020	52	41	complete	complete	ADJ
iajs-1020	52	42	arc	arc	NOUN
iajs-1020	52	43	if	if	SCONJ
iajs-1020	52	44	it	it	PRON
iajs-1020	52	45	is	be	AUX
iajs-1020	52	46	not	not	PART
iajs-1020	52	47	contained	contain	VERB
iajs-1020	52	48	in	in	ADP
iajs-1020	52	49	a	a	DET
iajs-1020	52	50	(	(	PUNCT
iajs-1020	52	51	k	k	X
iajs-1020	52	52	+	+	NOUN
iajs-1020	52	53	1,n)-arc	1,n)-arc	NUM
iajs-1020	52	54	.	.	PUNCT
iajs-1020	53	1	a	a	DET
iajs-1020	53	2	(	(	PUNCT
iajs-1020	53	3	k	k	NOUN
iajs-1020	53	4	,	,	PUNCT
iajs-1020	53	5	n)-arc	n)-arc	ADV
iajs-1020	53	6	in	in	ADP
iajs-1020	53	7	pg(2,q	pg(2,q	NOUN
iajs-1020	53	8	)	)	PUNCT
iajs-1020	53	9	is	be	AUX
iajs-1020	53	10	maximal	maximal	ADJ
iajs-1020	53	11	-	-	PUNCT
iajs-1020	53	12	arc	arc	NOUN
iajs-1020	53	13	if	if	SCONJ
iajs-1020	53	14	every	every	DET
iajs-1020	53	15	line	line	NOUN
iajs-1020	53	16	in	in	ADP
iajs-1020	53	17	pg(2,q	pg(2,q	NOUN
iajs-1020	53	18	)	)	PUNCT
iajs-1020	53	19	is	be	AUX
iajs-1020	53	20	a	a	DET
iajs-1020	53	21	zero	zero	NUM
iajs-1020	53	22	secant	secant	NOUN
iajs-1020	53	23	or	or	CCONJ
iajs-1020	53	24	an	an	DET
iajs-1020	53	25	n	n	CCONJ
iajs-1020	53	26	-	-	PUNCT
iajs-1020	53	27	secant	secant	NOUN
iajs-1020	53	28	of	of	ADP
iajs-1020	53	29	the	the	DET
iajs-1020	53	30	(	(	PUNCT
iajs-1020	53	31	k	k	NOUN
iajs-1020	53	32	,	,	PUNCT
iajs-1020	53	33	n)-arc	n)-arc	NOUN
iajs-1020	53	34	.	.	PUNCT
iajs-1020	54	1	2.10	2.10	NUM
iajs-1020	54	2	definition	definition	NOUN
iajs-1020	54	3	"	"	PUNCT
iajs-1020	54	4	flag"[1	flag"[1	PROPN
iajs-1020	54	5	]	]	X
iajs-1020	54	6	a	a	DET
iajs-1020	54	7	flag	flag	NOUN
iajs-1020	54	8	in	in	ADP
iajs-1020	54	9	pg(2,q	pg(2,q	NOUN
iajs-1020	54	10	)	)	PUNCT
iajs-1020	54	11	is	be	AUX
iajs-1020	54	12	an	an	DET
iajs-1020	54	13	incident	incident	NOUN
iajs-1020	54	14	point	point	NOUN
iajs-1020	54	15	-	-	PUNCT
iajs-1020	54	16	line	line	NOUN
iajs-1020	54	17	pair	pair	NOUN
iajs-1020	54	18	;	;	PUNCT
iajs-1020	54	19	flag	flag	NOUN
iajs-1020	54	20	=	=	SYM
iajs-1020	54	21	{	{	PUNCT
iajs-1020	54	22	(	(	PUNCT
iajs-1020	54	23	p	p	X
iajs-1020	54	24	i	i	PROPN
iajs-1020	54	25	,	,	PUNCT
iajs-1020	54	26	lj	lj	PROPN
iajs-1020	54	27	)	)	PUNCT
iajs-1020	54	28	;	;	PUNCT
iajs-1020	55	1	pi	pi	PROPN
iajs-1020	55	2			PROPN
iajs-1020	55	3	lj	lj	PROPN
iajs-1020	55	4	,	,	PUNCT
iajs-1020	55	5	i	i	PRON
iajs-1020	55	6	,	,	PUNCT
iajs-1020	55	7	j=1,2,	j=1,2,	NOUN
iajs-1020	55	8	…	…	SYM
iajs-1020	55	9	,q2	,q2	PUNCT
iajs-1020	55	10	+	+	NOUN
iajs-1020	55	11	q+1	q+1	ADJ
iajs-1020	55	12	}	}	PUNCT
iajs-1020	55	13	.	.	PUNCT
iajs-1020	56	1	2.11	2.11	NUM
iajs-1020	56	2	definition	definition	NOUN
iajs-1020	56	3	"	"	PUNCT
iajs-1020	56	4	strong	strong	ADJ
iajs-1020	56	5	representive	representive	ADJ
iajs-1020	56	6	system	system	NOUN
iajs-1020	56	7	"	"	PUNCT
iajs-1020	56	8	[	[	X
iajs-1020	56	9	1	1	X
iajs-1020	56	10	]	]	PUNCT
iajs-1020	56	11	a	a	DET
iajs-1020	56	12	set	set	NOUN
iajs-1020	56	13	s	s	X
iajs-1020	56	14	=	=	PUNCT
iajs-1020	56	15	{	{	PUNCT
iajs-1020	56	16	(	(	PUNCT
iajs-1020	56	17	p1,l1),(p2,l2),	p1,l1),(p2,l2),	PROPN
iajs-1020	56	18	…	…	SYM
iajs-1020	56	19	,(ps	,(ps	ADJ
iajs-1020	56	20	,	,	PUNCT
iajs-1020	56	21	ls	ls	PROPN
iajs-1020	56	22	)	)	PUNCT
iajs-1020	56	23	}	}	PUNCT
iajs-1020	56	24	of	of	ADP
iajs-1020	56	25	flags	flag	NOUN
iajs-1020	56	26	pi	pi	NOUN
iajs-1020	56	27			NOUN
iajs-1020	56	28	lj	lj	INTJ
iajs-1020	56	29			PROPN
iajs-1020	57	1	i	i	PRON
iajs-1020	57	2	=	=	PUNCT
iajs-1020	57	3	j	j	PROPN
iajs-1020	57	4	is	be	AUX
iajs-1020	57	5	a	a	DET
iajs-1020	57	6	strong	strong	ADJ
iajs-1020	57	7	representive	representive	ADJ
iajs-1020	57	8	system	system	NOUN
iajs-1020	57	9	.	.	PUNCT
iajs-1020	58	1	the	the	DET
iajs-1020	58	2	members	member	NOUN
iajs-1020	58	3	of	of	ADP
iajs-1020	58	4	strong	strong	ADJ
iajs-1020	58	5	represent	represent	VERB
iajs-1020	58	6	system	system	NOUN
iajs-1020	58	7	that	that	PRON
iajs-1020	58	8	s	s	NUM
iajs-1020	58	9			NUM
iajs-1020	58	10	q	q	NOUN
iajs-1020	58	11	q	q	X
iajs-1020	58	12	+1	+1	PROPN
iajs-1020	58	13	,	,	PUNCT
iajs-1020	58	14	with	with	ADP
iajs-1020	58	15	equality	equality	NOUN
iajs-1020	58	16	if	if	SCONJ
iajs-1020	58	17	and	and	CCONJ
iajs-1020	58	18	only	only	ADV
iajs-1020	58	19	if	if	SCONJ
iajs-1020	58	20	s	s	X
iajs-1020	58	21	consists	consist	VERB
iajs-1020	58	22	of	of	ADP
iajs-1020	58	23	incident	incident	NOUN
iajs-1020	58	24	point	point	NOUN
iajs-1020	58	25	-	-	PUNCT
iajs-1020	58	26	tangent	tangent	NOUN
iajs-1020	58	27	pairs	pair	NOUN
iajs-1020	58	28	of	of	ADP
iajs-1020	58	29	a	a	DET
iajs-1020	58	30	unital	unital	NOUN
iajs-1020	58	31	,	,	PUNCT
iajs-1020	58	32	we	we	PRON
iajs-1020	58	33	denoted	denote	VERB
iajs-1020	58	34	points	point	NOUN
iajs-1020	58	35	of	of	ADP
iajs-1020	58	36	s	s	NOUN
iajs-1020	58	37	by	by	ADP
iajs-1020	58	38	p(s	p(s	NOUN
iajs-1020	58	39	)	)	PUNCT
iajs-1020	58	40	and	and	CCONJ
iajs-1020	58	41	the	the	DET
iajs-1020	58	42	lines	line	NOUN
iajs-1020	58	43	of	of	ADP
iajs-1020	58	44	s	s	NOUN
iajs-1020	58	45	by	by	ADP
iajs-1020	58	46	l(s	l(s	PROPN
iajs-1020	58	47	)	)	PUNCT
iajs-1020	58	48	,	,	PUNCT
iajs-1020	58	49	p(s	p(s	PROPN
iajs-1020	58	50	)	)	PUNCT
iajs-1020	58	51	and	and	CCONJ
iajs-1020	58	52	l(s	l(s	PROPN
iajs-1020	58	53	)	)	PUNCT
iajs-1020	58	54	are	be	AUX
iajs-1020	58	55	called	call	VERB
iajs-1020	58	56	spacialy	spacialy	PROPN
iajs-1020	58	57	and	and	CCONJ
iajs-1020	58	58	the	the	DET
iajs-1020	58	59	others	other	NOUN
iajs-1020	58	60	are	be	AUX
iajs-1020	58	61	called	call	VERB
iajs-1020	58	62	ordinary	ordinary	ADJ
iajs-1020	58	63	s	s	PART
iajs-1020	58	64	is	be	AUX
iajs-1020	58	65	called	call	VERB
iajs-1020	58	66	maximal	maximal	ADJ
iajs-1020	58	67	if	if	SCONJ
iajs-1020	58	68	is	be	AUX
iajs-1020	58	69	not	not	PART
iajs-1020	58	70	part	part	NOUN
iajs-1020	58	71	of	of	ADP
iajs-1020	58	72	larger	large	ADJ
iajs-1020	58	73	-	-	PUNCT
iajs-1020	58	74	strong	strong	ADJ
iajs-1020	58	75	represent	represent	NOUN
iajs-1020	58	76	.	.	PUNCT
iajs-1020	59	1	2.12	2.12	NUM
iajs-1020	59	2	definition	definition	NOUN
iajs-1020	59	3	"	"	PUNCT
iajs-1020	59	4	complete	complete	ADJ
iajs-1020	59	5	nuclei	nucleus	NOUN
iajs-1020	59	6	set	set	VERB
iajs-1020	59	7	"	"	PUNCT
iajs-1020	59	8	"	"	PUNCT
iajs-1020	59	9	new	new	ADJ
iajs-1020	59	10	"	"	PUNCT
iajs-1020	59	11	let	let	VERB
iajs-1020	59	12	n(s	n(s	PROPN
iajs-1020	59	13	)	)	PUNCT
iajs-1020	59	14	be	be	AUX
iajs-1020	59	15	a	a	DET
iajs-1020	59	16	set	set	NOUN
iajs-1020	59	17	of	of	ADP
iajs-1020	59	18	all	all	DET
iajs-1020	59	19	nucleus	nucleus	ADJ
iajs-1020	59	20	points	point	NOUN
iajs-1020	59	21	of	of	ADP
iajs-1020	59	22	a	a	DET
iajs-1020	59	23	set	set	NOUN
iajs-1020	59	24	s	s	PRON
iajs-1020	59	25	in	in	ADP
iajs-1020	59	26	pg(2,q	pg(2,q	NOUN
iajs-1020	59	27	)	)	PUNCT
iajs-1020	59	28	,	,	PUNCT
iajs-1020	59	29	n(s	n(s	PROPN
iajs-1020	59	30	)	)	PUNCT
iajs-1020	59	31	,	,	PUNCT
iajs-1020	59	32	is	be	AUX
iajs-1020	59	33	called	call	VERB
iajs-1020	59	34	complete	complete	ADJ
iajs-1020	59	35	nuclei	nucleus	NOUN
iajs-1020	59	36	set	set	VERB
iajs-1020	59	37	if	if	SCONJ
iajs-1020	59	38	n(s	n(	NOUN
iajs-1020	59	39	)	)	PUNCT
iajs-1020	59	40	=	=	PUNCT
iajs-1020	59	41	pg(2,q	pg(2,q	PRON
iajs-1020	59	42	)	)	PUNCT
iajs-1020	59	43	\	\	NOUN
iajs-1020	59	44	s.	s.	PROPN
iajs-1020	59	45	3	3	NUM
iajs-1020	59	46	.	.	PUNCT
iajs-1020	60	1	the	the	DET
iajs-1020	60	2	relation	relation	NOUN
iajs-1020	60	3	between	between	ADP
iajs-1020	60	4	the	the	DET
iajs-1020	60	5	sets	set	NOUN
iajs-1020	60	6	s	s	VERB
iajs-1020	60	7	ubspace	ubspace	NOUN
iajs-1020	60	8	of	of	ADP
iajs-1020	60	9	pg(2q	pg(2q	NOUN
iajs-1020	60	10	)	)	PUNCT
iajs-1020	60	11	over	over	ADP
iajs-1020	60	12	gf(q	gf(q	NOUN
iajs-1020	60	13	)	)	PUNCT
iajs-1020	60	14	this	this	DET
iajs-1020	60	15	section	section	NOUN
iajs-1020	60	16	contains	contain	VERB
iajs-1020	60	17	theorems	theorem	NOUN
iajs-1020	60	18	to	to	PART
iajs-1020	60	19	show	show	VERB
iajs-1020	60	20	that	that	SCONJ
iajs-1020	60	21	some	some	DET
iajs-1020	60	22	relations	relation	NOUN
iajs-1020	60	23	between	between	ADP
iajs-1020	60	24	the	the	DET
iajs-1020	60	25	:	:	PUNCT
iajs-1020	60	26	blocking	block	VERB
iajs-1020	60	27	set	set	NOUN
iajs-1020	60	28	,	,	PUNCT
iajs-1020	60	29	(	(	PUNCT
iajs-1020	60	30	k	k	NOUN
iajs-1020	60	31	,	,	PUNCT
iajs-1020	60	32	n)-arc	n)-arc	NOUN
iajs-1020	60	33	,	,	PUNCT
iajs-1020	60	34	unital	unital	ADJ
iajs-1020	60	35	set	set	NOUN
iajs-1020	60	36	,	,	PUNCT
iajs-1020	60	37	nuclei	nucleus	NOUN
iajs-1020	60	38	set	set	VERB
iajs-1020	60	39	,	,	PUNCT
iajs-1020	60	40	strong	strong	ADJ
iajs-1020	60	41	representive	representive	ADJ
iajs-1020	60	42	system	system	NOUN
iajs-1020	60	43	and	and	CCONJ
iajs-1020	60	44	the	the	DET
iajs-1020	60	45	set	set	NOUN
iajs-1020	60	46	of	of	ADP
iajs-1020	60	47	type	type	NOUN
iajs-1020	60	48	(	(	PUNCT
iajs-1020	60	49	0,1,2,q+1	0,1,2,q+1	NUM
iajs-1020	60	50	)	)	PUNCT
iajs-1020	60	51	.	.	PUNCT
iajs-1020	61	1	ihjpas	ihjpas	PROPN
iajs-1020	61	2	theorem	theorem	VERB
iajs-1020	61	3	let	let	VERB
iajs-1020	61	4	n(s	n(s	NUM
iajs-1020	61	5	)	)	PUNCT
iajs-1020	61	6	be	be	AUX
iajs-1020	61	7	complete	complete	ADJ
iajs-1020	61	8	,	,	PUNCT
iajs-1020	61	9	then	then	ADV
iajs-1020	61	10	s	s	VERB
iajs-1020	61	11	is	be	AUX
iajs-1020	61	12	a	a	DET
iajs-1020	61	13	line	line	NOUN
iajs-1020	61	14	.	.	PUNCT
iajs-1020	62	1	proof	proof	NOUN
iajs-1020	62	2	:	:	PUNCT
iajs-1020	62	3	for	for	ADP
iajs-1020	62	4	every	every	DET
iajs-1020	62	5	point	point	NOUN
iajs-1020	62	6	p	p	NOUN
iajs-1020	62	7	in	in	ADP
iajs-1020	62	8	n(s	n(s	PROPN
iajs-1020	62	9	)	)	PUNCT
iajs-1020	62	10	,	,	PUNCT
iajs-1020	62	11	p	p	PROPN
iajs-1020	62	12	is	be	AUX
iajs-1020	62	13	a	a	DET
iajs-1020	62	14	nucleus	nucleus	ADJ
iajs-1020	62	15	point	point	NOUN
iajs-1020	62	16	of	of	ADP
iajs-1020	62	17	s	s	PROPN
iajs-1020	62	18	,	,	PUNCT
iajs-1020	62	19	then	then	ADV
iajs-1020	62	20	every	every	DET
iajs-1020	62	21	line	line	NOUN
iajs-1020	62	22	in	in	ADP
iajs-1020	62	23	pg(2,q	pg(2,q	NOUN
iajs-1020	62	24	)	)	PUNCT
iajs-1020	62	25	through	through	ADP
iajs-1020	62	26	p	p	NOUN
iajs-1020	62	27	meets	meet	VERB
iajs-1020	62	28	s	s	NOUN
iajs-1020	62	29	in	in	ADP
iajs-1020	62	30	exactly	exactly	ADV
iajs-1020	62	31	one	one	NUM
iajs-1020	62	32	point	point	NOUN
iajs-1020	62	33	.	.	PUNCT
iajs-1020	63	1	since	since	SCONJ
iajs-1020	63	2	there	there	PRON
iajs-1020	63	3	exists	exist	VERB
iajs-1020	63	4	q	q	NOUN
iajs-1020	63	5	+	+	CCONJ
iajs-1020	63	6	1	1	NUM
iajs-1020	63	7	lines	line	NOUN
iajs-1020	63	8	through	through	ADP
iajs-1020	63	9	p	p	NOUN
iajs-1020	63	10	,	,	PUNCT
iajs-1020	63	11	then	then	ADV
iajs-1020	63	12	there	there	PRON
iajs-1020	63	13	exists	exist	VERB
iajs-1020	63	14	at	at	ADP
iajs-1020	63	15	least	least	ADJ
iajs-1020	63	16	q	q	NOUN
iajs-1020	64	1	+	+	CCONJ
iajs-1020	64	2	1	1	NUM
iajs-1020	64	3	points	point	NOUN
iajs-1020	64	4	in	in	ADP
iajs-1020	64	5	s.	s.	PROPN
iajs-1020	64	6	if	if	SCONJ
iajs-1020	64	7	there	there	PRON
iajs-1020	64	8	exists	exist	VERB
iajs-1020	64	9	another	another	DET
iajs-1020	64	10	point	point	NOUN
iajs-1020	64	11	r	r	NOUN
iajs-1020	64	12	in	in	ADP
iajs-1020	64	13	s	s	PROPN
iajs-1020	64	14	,	,	PUNCT
iajs-1020	64	15	then	then	ADV
iajs-1020	64	16	there	there	PRON
iajs-1020	64	17	exists	exist	VERB
iajs-1020	64	18	another	another	DET
iajs-1020	64	19	line	line	NOUN
iajs-1020	64	20	through	through	ADP
iajs-1020	64	21	p	p	NOUN
iajs-1020	64	22	and	and	CCONJ
iajs-1020	64	23	r	r	NOUN
iajs-1020	64	24	in	in	ADP
iajs-1020	64	25	s	s	PRON
iajs-1020	64	26	then	then	ADV
iajs-1020	64	27	there	there	PRON
iajs-1020	64	28	exists	exist	VERB
iajs-1020	64	29	another	another	DET
iajs-1020	64	30	line	line	NOUN
iajs-1020	64	31	through	through	ADP
iajs-1020	64	32	p	p	NOUN
iajs-1020	64	33	and	and	CCONJ
iajs-1020	64	34	r	r	NOUN
iajs-1020	64	35	,	,	PUNCT
iajs-1020	64	36	which	which	PRON
iajs-1020	64	37	is	be	AUX
iajs-1020	64	38	a	a	DET
iajs-1020	64	39	contradiction	contradiction	NOUN
iajs-1020	64	40	since	since	SCONJ
iajs-1020	64	41	there	there	PRON
iajs-1020	64	42	exists	exist	VERB
iajs-1020	64	43	exactly	exactly	ADV
iajs-1020	64	44	q	q	PUNCT
iajs-1020	64	45	+	+	NUM
iajs-1020	64	46	1	1	NUM
iajs-1020	64	47	lines	line	NOUN
iajs-1020	64	48	through	through	ADP
iajs-1020	64	49	p.	p.	NOUN
iajs-1020	64	50	hence	hence	ADV
iajs-1020	64	51	s	s	PART
iajs-1020	64	52	contains	contain	VERB
iajs-1020	64	53	exactly	exactly	ADV
iajs-1020	64	54	q	q	PUNCT
iajs-1020	64	55	+	+	CCONJ
iajs-1020	64	56	1	1	NUM
iajs-1020	64	57	points	point	NOUN
iajs-1020	64	58	p1	p1	NOUN
iajs-1020	64	59	,	,	PUNCT
iajs-1020	64	60	…	…	PUNCT
iajs-1020	64	61	,	,	PUNCT
iajs-1020	65	1	pq	pq	PROPN
iajs-1020	65	2	+	+	CCONJ
iajs-1020	65	3	1	1	NUM
iajs-1020	65	4	,	,	PUNCT
iajs-1020	65	5	suppose	suppose	VERB
iajs-1020	65	6	these	these	DET
iajs-1020	65	7	points	point	NOUN
iajs-1020	65	8	are	be	AUX
iajs-1020	65	9	not	not	PART
iajs-1020	65	10	collinear	collinear	ADJ
iajs-1020	65	11	,	,	PUNCT
iajs-1020	65	12	then	then	ADV
iajs-1020	65	13			VERB
iajs-1020	65	14	at	at	ADV
iajs-1020	65	15	least	least	ADV
iajs-1020	65	16	one	one	NUM
iajs-1020	65	17	point	point	NOUN
iajs-1020	65	18	,	,	PUNCT
iajs-1020	65	19	say	say	VERB
iajs-1020	65	20	pq	pq	INTJ
iajs-1020	66	1	+	+	ADV
iajs-1020	66	2	1	1	NUM
iajs-1020	66	3	,	,	PUNCT
iajs-1020	66	4	not	not	PART
iajs-1020	66	5	collinear	collinear	ADJ
iajs-1020	66	6	with	with	ADP
iajs-1020	66	7	two	two	NUM
iajs-1020	66	8	points	point	NOUN
iajs-1020	66	9	say	say	VERB
iajs-1020	66	10	p1	p1	NOUN
iajs-1020	66	11	and	and	CCONJ
iajs-1020	66	12	p2	p2	NOUN
iajs-1020	66	13	,	,	PUNCT
iajs-1020	66	14	the	the	DET
iajs-1020	66	15	line	line	NOUN
iajs-1020	66	16	ppq	ppq	PROPN
iajs-1020	66	17	+	+	CCONJ
iajs-1020	66	18	1	1	NUM
iajs-1020	66	19	intersects	intersect	VERB
iajs-1020	66	20	the	the	DET
iajs-1020	66	21	line	line	NOUN
iajs-1020	66	22	p1p2	p1p2	PROPN
iajs-1020	66	23	in	in	ADP
iajs-1020	66	24	one	one	NUM
iajs-1020	66	25	point	point	NOUN
iajs-1020	66	26	,	,	PUNCT
iajs-1020	66	27	say	say	VERB
iajs-1020	66	28	pq	pq	VERB
iajs-1020	66	29	+2	+2	PROPN
iajs-1020	66	30	,	,	PUNCT
iajs-1020	66	31	pq	pq	INTJ
iajs-1020	66	32	+2	+2	PROPN
iajs-1020	66	33	is	be	AUX
iajs-1020	66	34	on	on	ADP
iajs-1020	66	35	the	the	DET
iajs-1020	66	36	line	line	NOUN
iajs-1020	67	1	p1p2	p1p2	PROPN
iajs-1020	67	2	,	,	PUNCT
iajs-1020	67	3	then	then	ADV
iajs-1020	67	4	pq	pq	INTJ
iajs-1020	67	5	+2	+2	PROPN
iajs-1020	67	6	is	be	AUX
iajs-1020	67	7	not	not	PART
iajs-1020	67	8	on	on	ADP
iajs-1020	67	9	s	s	PRON
iajs-1020	67	10	hence	hence	ADV
iajs-1020	67	11	the	the	DET
iajs-1020	67	12	line	line	NOUN
iajs-1020	67	13	ppq	ppq	PROPN
iajs-1020	68	1	+	+	CCONJ
iajs-1020	68	2	1	1	NUM
iajs-1020	68	3	,	,	PUNCT
iajs-1020	68	4	since	since	SCONJ
iajs-1020	68	5	the	the	DET
iajs-1020	68	6	line	line	NOUN
iajs-1020	68	7	ppq	ppq	PROPN
iajs-1020	68	8	+	+	CCONJ
iajs-1020	68	9	1	1	NUM
iajs-1020	68	10	intersects	intersect	NOUN
iajs-1020	68	11	s	s	PRON
iajs-1020	68	12	in	in	ADP
iajs-1020	68	13	only	only	ADV
iajs-1020	68	14	one	one	NUM
iajs-1020	68	15	point	point	NOUN
iajs-1020	69	1	pq	pq	INTJ
iajs-1020	70	1	+	+	CCONJ
iajs-1020	70	2	1	1	X
iajs-1020	70	3	.	.	X
iajs-1020	71	1	pq	pq	NOUN
iajs-1020	72	1	+	+	CCONJ
iajs-1020	72	2	2	2	NUM
iajs-1020	72	3	is	be	AUX
iajs-1020	72	4	not	not	PART
iajs-1020	72	5	in	in	ADP
iajs-1020	72	6	s	s	PROPN
iajs-1020	72	7	,	,	PUNCT
iajs-1020	72	8	then	then	ADV
iajs-1020	72	9	any	any	DET
iajs-1020	72	10	line	line	NOUN
iajs-1020	72	11	through	through	ADP
iajs-1020	72	12	it	it	PRON
iajs-1020	72	13	intersects	intersect	VERB
iajs-1020	72	14	s	s	NOUN
iajs-1020	72	15	in	in	ADP
iajs-1020	72	16	one	one	NUM
iajs-1020	72	17	point	point	NOUN
iajs-1020	72	18	but	but	CCONJ
iajs-1020	72	19	the	the	DET
iajs-1020	72	20	line	line	NOUN
iajs-1020	72	21	p1p2	p1p2	X
iajs-1020	72	22	which	which	PRON
iajs-1020	72	23	passing	pass	VERB
iajs-1020	72	24	pq	pq	NOUN
iajs-1020	72	25	+2	+2	PROPN
iajs-1020	72	26	intersects	intersect	NOUN
iajs-1020	72	27	s	s	PRON
iajs-1020	72	28	in	in	ADP
iajs-1020	72	29	two	two	NUM
iajs-1020	72	30	points	point	NOUN
iajs-1020	72	31	which	which	PRON
iajs-1020	72	32	is	be	AUX
iajs-1020	72	33	a	a	DET
iajs-1020	72	34	contradiction	contradiction	NOUN
iajs-1020	72	35	.	.	PUNCT
iajs-1020	73	1	hence	hence	ADV
iajs-1020	73	2	the	the	DET
iajs-1020	73	3	points	point	NOUN
iajs-1020	73	4	p1	p1	NOUN
iajs-1020	73	5	,	,	PUNCT
iajs-1020	73	6	p2	p2	NOUN
iajs-1020	73	7	,	,	PUNCT
iajs-1020	73	8	…	…	PUNCT
iajs-1020	73	9	,	,	PUNCT
iajs-1020	73	10	pq	pq	NOUN
iajs-1020	74	1	+	+	CCONJ
iajs-1020	74	2	1	1	NUM
iajs-1020	74	3	are	be	AUX
iajs-1020	74	4	collinear	collinear	ADJ
iajs-1020	74	5	,	,	PUNCT
iajs-1020	74	6	similarly	similarly	ADV
iajs-1020	74	7	for	for	ADP
iajs-1020	74	8	any	any	DET
iajs-1020	74	9	three	three	NUM
iajs-1020	74	10	points	point	NOUN
iajs-1020	74	11	p1	p1	NOUN
iajs-1020	74	12	,	,	PUNCT
iajs-1020	74	13	p2	p2	NOUN
iajs-1020	74	14	,	,	PUNCT
iajs-1020	74	15	…	…	PUNCT
iajs-1020	74	16	,	,	PUNCT
iajs-1020	74	17	pq	pq	NOUN
iajs-1020	75	1	+	+	CCONJ
iajs-1020	75	2	1	1	NUM
iajs-1020	75	3	are	be	AUX
iajs-1020	75	4	collinear	collinear	VERB
iajs-1020	75	5	.	.	PUNCT
iajs-1020	76	1	theorem	theorem	PROPN
iajs-1020	76	2	[	[	X
iajs-1020	76	3	1	1	NUM
iajs-1020	76	4	]	]	PUNCT
iajs-1020	76	5	"	"	PUNCT
iajs-1020	76	6	without	without	ADP
iajs-1020	76	7	prove	prove	NOUN
iajs-1020	76	8	"	"	PUNCT
iajs-1020	76	9	let	let	VERB
iajs-1020	76	10	b	b	X
iajs-1020	76	11	be	be	AUX
iajs-1020	76	12	a	a	DET
iajs-1020	76	13	blocking	blocking	NOUN
iajs-1020	76	14	in	in	ADP
iajs-1020	76	15	pg(2,q	pg(2,q	NOUN
iajs-1020	76	16	)	)	PUNCT
iajs-1020	76	17	,	,	PUNCT
iajs-1020	76	18	then	then	ADV
iajs-1020	76	19	for	for	ADP
iajs-1020	76	20	every	every	DET
iajs-1020	76	21	p	p	NOUN
iajs-1020	76	22	pg(2,q	pg(2,q	NOUN
iajs-1020	76	23	)	)	PUNCT
iajs-1020	76	24	\b	\b	NOUN
iajs-1020	76	25	,	,	PUNCT
iajs-1020	76	26	p	p	PROPN
iajs-1020	76	27	is	be	AUX
iajs-1020	76	28	t	t	NOUN
iajs-1020	76	29	-	-	ADJ
iajs-1020	76	30	fold	fold	ADJ
iajs-1020	76	31	nucleus	nucleus	ADJ
iajs-1020	76	32	point	point	NOUN
iajs-1020	76	33	,	,	PUNCT
iajs-1020	76	34	if	if	SCONJ
iajs-1020	76	35	and	and	CCONJ
iajs-1020	76	36	only	only	ADV
iajs-1020	76	37	if	if	SCONJ
iajs-1020	76	38	b	b	NOUN
iajs-1020	76	39	is	be	AUX
iajs-1020	76	40	a	a	DET
iajs-1020	76	41	t	t	NOUN
iajs-1020	76	42	-	-	PUNCT
iajs-1020	76	43	fold	fold	ADJ
iajs-1020	76	44	blocking	blocking	NOUN
iajs-1020	76	45	set	set	NOUN
iajs-1020	76	46	,	,	PUNCT
iajs-1020	76	47	2	2	NUM
iajs-1020	76	48			NOUN
iajs-1020	76	49	t	t	NOUN
iajs-1020	76	50			NUM
iajs-1020	76	51	q.	q.	NOUN
iajs-1020	76	52	proof	proof	NOUN
iajs-1020	76	53	:	:	PUNCT
iajs-1020	76	54	suppose	suppose	VERB
iajs-1020	76	55	that	that	SCONJ
iajs-1020	76	56	b	b	PROPN
iajs-1020	76	57	is	be	AUX
iajs-1020	76	58	a	a	DET
iajs-1020	76	59	blocking	blocking	NOUN
iajs-1020	76	60	set	set	NOUN
iajs-1020	76	61	and	and	CCONJ
iajs-1020	76	62	every	every	DET
iajs-1020	76	63	p	p	NOUN
iajs-1020	76	64	pg(2,q	pg(2,q	VERB
iajs-1020	76	65	)	)	PUNCT
iajs-1020	76	66	\b	\b	NOUN
iajs-1020	76	67	,	,	PUNCT
iajs-1020	76	68	p	p	NOUN
iajs-1020	76	69	is	be	AUX
iajs-1020	76	70	a	a	DET
iajs-1020	76	71	t	t	NOUN
iajs-1020	76	72	-	-	PUNCT
iajs-1020	76	73	fold	fold	NOUN
iajs-1020	76	74	blocking	block	VERB
iajs-1020	76	75	nucleus	nucleus	ADJ
iajs-1020	76	76	point	point	NOUN
iajs-1020	76	77	of	of	ADP
iajs-1020	76	78	b	b	PROPN
iajs-1020	76	79	,	,	PUNCT
iajs-1020	76	80	then	then	ADV
iajs-1020	76	81	every	every	DET
iajs-1020	76	82	line	line	NOUN
iajs-1020	76	83	in	in	ADP
iajs-1020	76	84	pg(2,q	pg(2,q	NOUN
iajs-1020	76	85	)	)	PUNCT
iajs-1020	76	86	through	through	ADP
iajs-1020	76	87	p	p	NOUN
iajs-1020	76	88	meets	meet	VERB
iajs-1020	76	89	b	b	NOUN
iajs-1020	76	90	in	in	ADP
iajs-1020	76	91	at	at	ADV
iajs-1020	76	92	least	least	ADJ
iajs-1020	76	93	t	t	NOUN
iajs-1020	76	94	points	point	NOUN
iajs-1020	76	95	,	,	PUNCT
iajs-1020	76	96	but	but	CCONJ
iajs-1020	76	97	from	from	ADP
iajs-1020	76	98	definition	definition	NOUN
iajs-1020	76	99	of	of	ADP
iajs-1020	76	100	blocking	block	VERB
iajs-1020	76	101	set	set	NOUN
iajs-1020	76	102	b	b	NOUN
iajs-1020	76	103	can	can	AUX
iajs-1020	76	104	not	not	PART
iajs-1020	76	105	contain	contain	VERB
iajs-1020	76	106	any	any	DET
iajs-1020	76	107	line	line	NOUN
iajs-1020	76	108	,	,	PUNCT
iajs-1020	76	109	so	so	CCONJ
iajs-1020	76	110	every	every	DET
iajs-1020	76	111	line	line	NOUN
iajs-1020	76	112	in	in	ADP
iajs-1020	76	113	pg(2,q	pg(2,q	NOUN
iajs-1020	76	114	)	)	PUNCT
iajs-1020	76	115	meets	meet	VERB
iajs-1020	76	116	b	b	NOUN
iajs-1020	76	117	in	in	ADP
iajs-1020	76	118	at	at	ADV
iajs-1020	76	119	least	least	ADJ
iajs-1020	76	120	t	t	NOUN
iajs-1020	76	121	points	point	NOUN
iajs-1020	76	122	,	,	PUNCT
iajs-1020	76	123	then	then	ADV
iajs-1020	76	124	b	b	PROPN
iajs-1020	76	125	is	be	AUX
iajs-1020	76	126	a	a	DET
iajs-1020	76	127	t	t	NOUN
iajs-1020	76	128	-	-	PUNCT
iajs-1020	76	129	fold	fold	ADJ
iajs-1020	76	130	blocking	blocking	NOUN
iajs-1020	76	131	set	set	NOUN
iajs-1020	76	132	.	.	PUNCT
iajs-1020	77	1	conversely	conversely	ADV
iajs-1020	77	2	,	,	PUNCT
iajs-1020	77	3	suppose	suppose	VERB
iajs-1020	77	4	b	b	X
iajs-1020	77	5	is	be	AUX
iajs-1020	77	6	a	a	DET
iajs-1020	77	7	t	t	NOUN
iajs-1020	77	8	-	-	PUNCT
iajs-1020	77	9	fold	fold	ADJ
iajs-1020	77	10	blocking	blocking	NOUN
iajs-1020	77	11	set	set	NOUN
iajs-1020	77	12	then	then	ADV
iajs-1020	77	13	every	every	DET
iajs-1020	77	14	line	line	NOUN
iajs-1020	77	15	in	in	ADP
iajs-1020	77	16	pg(2,q	pg(2,q	NOUN
iajs-1020	77	17	)	)	PUNCT
iajs-1020	77	18	meets	meet	VERB
iajs-1020	77	19	b	b	NOUN
iajs-1020	77	20	in	in	ADP
iajs-1020	77	21	at	at	ADV
iajs-1020	77	22	least	least	ADJ
iajs-1020	77	23	t	t	NOUN
iajs-1020	77	24	points	point	NOUN
iajs-1020	77	25	,	,	PUNCT
iajs-1020	77	26	then	then	ADV
iajs-1020	77	27	for	for	ADP
iajs-1020	77	28	every	every	DET
iajs-1020	77	29	point	point	NOUN
iajs-1020	77	30	p	p	NOUN
iajs-1020	77	31	pg(2,q	pg(2,q	NOUN
iajs-1020	77	32	)	)	PUNCT
iajs-1020	77	33	\b	\b	NOUN
iajs-1020	77	34	and	and	CCONJ
iajs-1020	77	35	every	every	DET
iajs-1020	77	36	line	line	NOUN
iajs-1020	77	37	through	through	ADP
iajs-1020	77	38	p	p	NOUN
iajs-1020	77	39	intersects	intersect	NOUN
iajs-1020	77	40	b	b	NOUN
iajs-1020	77	41	in	in	ADP
iajs-1020	77	42	at	at	ADV
iajs-1020	77	43	least	least	ADJ
iajs-1020	77	44	tpoints	tpoint	NOUN
iajs-1020	77	45	,	,	PUNCT
iajs-1020	77	46	then	then	ADV
iajs-1020	77	47	for	for	ADP
iajs-1020	77	48	every	every	DET
iajs-1020	77	49	p	p	NOUN
iajs-1020	77	50	pg(2,q	pg(2,q	NOUN
iajs-1020	77	51	)	)	PUNCT
iajs-1020	77	52	\b	\b	NOUN
iajs-1020	77	53	,	,	PUNCT
iajs-1020	77	54	p	p	NOUN
iajs-1020	77	55	is	be	AUX
iajs-1020	77	56	a	a	DET
iajs-1020	77	57	t	t	NOUN
iajs-1020	77	58	-	-	ADJ
iajs-1020	77	59	fold	fold	ADJ
iajs-1020	77	60	nucleus	nucleus	ADJ
iajs-1020	77	61	point	point	NOUN
iajs-1020	77	62	.	.	PUNCT
iajs-1020	78	1	theorem	theorem	VERB
iajs-1020	78	2	in	in	ADP
iajs-1020	78	3	pg(2,q	pg(2,q	NOUN
iajs-1020	78	4	)	)	PUNCT
iajs-1020	78	5	,	,	PUNCT
iajs-1020	78	6	q	q	NOUN
iajs-1020	79	1	=	=	PUNCT
iajs-1020	79	2	p	p	NOUN
iajs-1020	79	3	2	2	NUM
iajs-1020	79	4	,	,	PUNCT
iajs-1020	79	5	every	every	DET
iajs-1020	79	6	unital	unital	ADJ
iajs-1020	79	7	set	set	NOUN
iajs-1020	79	8	is	be	AUX
iajs-1020	79	9	a	a	DET
iajs-1020	79	10	(	(	PUNCT
iajs-1020	79	11	qp+1,p+1)-arc	qp+1,p+1)-arc	NOUN
iajs-1020	79	12	,	,	PUNCT
iajs-1020	79	13	q	q	X
iajs-1020	79	14			NUM
iajs-1020	79	15	3	3	NUM
iajs-1020	79	16	.	.	PUNCT
iajs-1020	80	1	proof	proof	NOUN
iajs-1020	80	2	:	:	PUNCT
iajs-1020	80	3	let	let	VERB
iajs-1020	80	4	u	u	PRON
iajs-1020	80	5	be	be	AUX
iajs-1020	80	6	a	a	DET
iajs-1020	80	7	unital	unital	ADJ
iajs-1020	80	8	set	set	NOUN
iajs-1020	80	9	in	in	ADP
iajs-1020	80	10	pg(2,q	pg(2,q	NOUN
iajs-1020	80	11	)	)	PUNCT
iajs-1020	80	12	,	,	PUNCT
iajs-1020	80	13	q	q	NOUN
iajs-1020	80	14	=	=	NOUN
iajs-1020	80	15	p2	p2	PROPN
iajs-1020	80	16	then	then	ADV
iajs-1020	80	17	every	every	DET
iajs-1020	80	18	line	line	NOUN
iajs-1020	80	19	in	in	ADP
iajs-1020	80	20	pg(2,q	pg(2,q	NOUN
iajs-1020	80	21	)	)	PUNCT
iajs-1020	80	22	,	,	PUNCT
iajs-1020	80	23	q	q	NOUN
iajs-1020	80	24	=	=	VERB
iajs-1020	80	25	p2	p2	PROPN
iajs-1020	80	26	intersects	intersect	NOUN
iajs-1020	80	27	u	u	NOUN
iajs-1020	80	28	in	in	ADP
iajs-1020	80	29	either	either	DET
iajs-1020	80	30	1	1	NUM
iajs-1020	80	31	or	or	CCONJ
iajs-1020	80	32	p	p	NOUN
iajs-1020	80	33	+	+	CCONJ
iajs-1020	80	34	1	1	NUM
iajs-1020	80	35	points	point	NOUN
iajs-1020	80	36	and	and	CCONJ
iajs-1020	80	37	u	u	NOUN
iajs-1020	80	38	is	be	AUX
iajs-1020	80	39	a	a	DET
iajs-1020	80	40	set	set	NOUN
iajs-1020	80	41	of	of	ADP
iajs-1020	80	42	qp	qp	NOUN
iajs-1020	80	43	+	+	CCONJ
iajs-1020	80	44	1	1	NUM
iajs-1020	80	45	points	point	NOUN
iajs-1020	81	1	and	and	CCONJ
iajs-1020	81	2	there	there	PRON
iajs-1020	81	3	are	be	VERB
iajs-1020	81	4	no	no	DET
iajs-1020	81	5	p	p	NOUN
iajs-1020	82	1	+	+	NOUN
iajs-1020	82	2	2	2	NUM
iajs-1020	82	3	points	point	NOUN
iajs-1020	82	4	are	be	AUX
iajs-1020	82	5	collinear	collinear	ADJ
iajs-1020	82	6	then	then	ADV
iajs-1020	82	7	u	u	NOUN
iajs-1020	82	8	is	be	AUX
iajs-1020	82	9	(	(	PUNCT
iajs-1020	82	10	pq+1,p+1)-arc	pq+1,p+1)-arc	X
iajs-1020	82	11	.	.	PUNCT
iajs-1020	83	1	the	the	DET
iajs-1020	83	2	converse	converse	NOUN
iajs-1020	83	3	is	be	AUX
iajs-1020	83	4	not	not	PART
iajs-1020	83	5	true	true	ADJ
iajs-1020	83	6	as	as	SCONJ
iajs-1020	83	7	shown	show	VERB
iajs-1020	83	8	by	by	ADP
iajs-1020	83	9	the	the	DET
iajs-1020	83	10	following	follow	VERB
iajs-1020	83	11	example	example	NOUN
iajs-1020	83	12	:	:	PUNCT
iajs-1020	83	13	in	in	ADP
iajs-1020	83	14	projective	projective	ADJ
iajs-1020	83	15	plan	plan	PROPN
iajs-1020	83	16	pg(2,4	pg(2,4	PROPN
iajs-1020	83	17	)	)	PUNCT
iajs-1020	83	18	,	,	PUNCT
iajs-1020	83	19	let	let	VERB
iajs-1020	83	20	k	k	PROPN
iajs-1020	83	21	=	=	PUNCT
iajs-1020	83	22	{	{	PUNCT
iajs-1020	83	23	1,2,3,4,7,8,11,12,13,15,16,21	1,2,3,4,7,8,11,12,13,15,16,21	NUM
iajs-1020	83	24	}	}	PUNCT
iajs-1020	83	25	,	,	PUNCT
iajs-1020	83	26	k	k	PROPN
iajs-1020	83	27	is	be	AUX
iajs-1020	83	28	an	an	DET
iajs-1020	83	29	(	(	PUNCT
iajs-1020	83	30	12,4)-arc	12,4)-arc	NUM
iajs-1020	83	31	,	,	PUNCT
iajs-1020	83	32	then	then	ADV
iajs-1020	83	33	k	k	PROPN
iajs-1020	83	34	is	be	AUX
iajs-1020	83	35	not	not	PART
iajs-1020	83	36	a	a	DET
iajs-1020	83	37	unital	unital	ADJ
iajs-1020	83	38	set	set	NOUN
iajs-1020	83	39	since	since	SCONJ
iajs-1020	83	40	:	:	PUNCT
iajs-1020	84	1	1	1	X
iajs-1020	84	2	.	.	X
iajs-1020	85	1	every	every	DET
iajs-1020	85	2	unital	unital	ADJ
iajs-1020	85	3	in	in	ADP
iajs-1020	85	4	pg(2,q	pg(2,q	NOUN
iajs-1020	85	5	)	)	PUNCT
iajs-1020	85	6	contains	contain	VERB
iajs-1020	85	7	(	(	PUNCT
iajs-1020	85	8	9	9	NUM
iajs-1020	85	9	)	)	PUNCT
iajs-1020	85	10	points	point	NOUN
iajs-1020	85	11	,	,	PUNCT
iajs-1020	85	12	but	but	CCONJ
iajs-1020	85	13	(	(	PUNCT
iajs-1020	85	14	k,4)-arc	k,4)-arc	X
iajs-1020	85	15	contains	contain	VERB
iajs-1020	85	16	(	(	PUNCT
iajs-1020	85	17	12	12	NUM
iajs-1020	85	18	)	)	PUNCT
iajs-1020	85	19	points	point	NOUN
iajs-1020	85	20	.	.	PUNCT
iajs-1020	86	1	2	2	X
iajs-1020	86	2	.	.	X
iajs-1020	86	3	some	some	DET
iajs-1020	86	4	line	line	NOUN
iajs-1020	86	5	in	in	ADP
iajs-1020	86	6	pg(2,4	pg(2,4	NOUN
iajs-1020	86	7	)	)	PUNCT
iajs-1020	86	8	meets	meet	VERB
iajs-1020	86	9	(	(	PUNCT
iajs-1020	86	10	k,4)-arc	k,4)-arc	X
iajs-1020	86	11	in	in	ADP
iajs-1020	86	12	4	4	NUM
iajs-1020	86	13	points	point	NOUN
iajs-1020	86	14	,	,	PUNCT
iajs-1020	86	15	but	but	CCONJ
iajs-1020	86	16	every	every	DET
iajs-1020	86	17	line	line	NOUN
iajs-1020	86	18	in	in	ADP
iajs-1020	86	19	pg(2,4	pg(2,4	NOUN
iajs-1020	86	20	)	)	PUNCT
iajs-1020	87	1	most	most	ADJ
iajs-1020	87	2	meets	meet	VERB
iajs-1020	87	3	every	every	DET
iajs-1020	87	4	unital	unital	ADJ
iajs-1020	87	5	set	set	NOUN
iajs-1020	87	6	in	in	ADP
iajs-1020	87	7	either	either	PRON
iajs-1020	87	8	1	1	NUM
iajs-1020	87	9	or	or	CCONJ
iajs-1020	87	10	3	3	NUM
iajs-1020	87	11	points	point	NOUN
iajs-1020	87	12	.	.	PUNCT
iajs-1020	88	1	3	3	X
iajs-1020	88	2	.	.	X
iajs-1020	88	3	theorem	theorem	VERB
iajs-1020	88	4	in	in	ADP
iajs-1020	88	5	pg(2,q	pg(2,q	NOUN
iajs-1020	88	6	)	)	PUNCT
iajs-1020	88	7	,	,	PUNCT
iajs-1020	88	8	q	q	NOUN
iajs-1020	89	1	=	=	PUNCT
iajs-1020	89	2	p	p	NOUN
iajs-1020	89	3	2	2	NUM
iajs-1020	89	4	every	every	DET
iajs-1020	89	5	unital	unital	ADJ
iajs-1020	89	6	set	set	NOUN
iajs-1020	89	7	is	be	AUX
iajs-1020	89	8	a	a	DET
iajs-1020	89	9	blocking	block	VERB
iajs-1020	89	10	set	set	NOUN
iajs-1020	89	11	.	.	PUNCT
iajs-1020	90	1	proof	proof	NOUN
iajs-1020	90	2	:	:	PUNCT
iajs-1020	90	3	let	let	VERB
iajs-1020	90	4	u	u	PRON
iajs-1020	90	5	be	be	AUX
iajs-1020	90	6	a	a	DET
iajs-1020	90	7	unital	unital	ADJ
iajs-1020	90	8	set	set	NOUN
iajs-1020	90	9	in	in	ADP
iajs-1020	90	10	pg(2,q	pg(2,q	NOUN
iajs-1020	90	11	)	)	PUNCT
iajs-1020	90	12	,	,	PUNCT
iajs-1020	90	13	q	q	NOUN
iajs-1020	91	1	=	=	PUNCT
iajs-1020	91	2	p	p	NOUN
iajs-1020	91	3	2	2	NUM
iajs-1020	91	4	then	then	ADV
iajs-1020	91	5	u	u	NOUN
iajs-1020	91	6	contains	contain	VERB
iajs-1020	91	7	qp+1	qp+1	NOUN
iajs-1020	91	8	points	point	NOUN
iajs-1020	91	9	and	and	CCONJ
iajs-1020	91	10	every	every	DET
iajs-1020	91	11	line	line	NOUN
iajs-1020	91	12	in	in	ADP
iajs-1020	91	13	pg(2,q	pg(2,q	NOUN
iajs-1020	91	14	)	)	PUNCT
iajs-1020	91	15	,	,	PUNCT
iajs-1020	91	16	q	q	NOUN
iajs-1020	92	1	=	=	SYM
iajs-1020	92	2	p	p	SYM
iajs-1020	92	3	2	2	NUM
iajs-1020	92	4	intersects	intersect	NOUN
iajs-1020	92	5	u	u	NOUN
iajs-1020	92	6	in	in	ADP
iajs-1020	92	7	either	either	DET
iajs-1020	92	8	1	1	NUM
iajs-1020	92	9	or	or	CCONJ
iajs-1020	92	10	p	p	NOUN
iajs-1020	92	11	+	+	CCONJ
iajs-1020	92	12	1	1	NUM
iajs-1020	92	13	points	point	NOUN
iajs-1020	92	14	so	so	SCONJ
iajs-1020	92	15	every	every	DET
iajs-1020	92	16	line	line	NOUN
iajs-1020	92	17	in	in	ADP
iajs-1020	92	18	pg(2,q	pg(2,q	NOUN
iajs-1020	92	19	)	)	PUNCT
iajs-1020	92	20	,	,	PUNCT
iajs-1020	92	21	q	q	NOUN
iajs-1020	92	22	=	=	VERB
iajs-1020	92	23	p2	p2	PROPN
iajs-1020	92	24	meets	meet	VERB
iajs-1020	92	25	u	u	NOUN
iajs-1020	92	26	,	,	PUNCT
iajs-1020	92	27	but	but	CCONJ
iajs-1020	92	28	u	u	NOUN
iajs-1020	92	29	dose	dose	AUX
iajs-1020	92	30	not	not	PART
iajs-1020	92	31	contain	contain	VERB
iajs-1020	92	32	any	any	DET
iajs-1020	92	33	line	line	NOUN
iajs-1020	92	34	;	;	PUNCT
iajs-1020	92	35	then	then	ADV
iajs-1020	92	36	u	u	NOUN
iajs-1020	92	37	is	be	AUX
iajs-1020	92	38	a	a	DET
iajs-1020	92	39	blocking	block	VERB
iajs-1020	92	40	set	set	NOUN
iajs-1020	92	41	.	.	PUNCT
iajs-1020	93	1	the	the	DET
iajs-1020	93	2	converse	converse	NOUN
iajs-1020	93	3	is	be	AUX
iajs-1020	93	4	not	not	PART
iajs-1020	93	5	true	true	ADJ
iajs-1020	93	6	and	and	CCONJ
iajs-1020	93	7	showed	show	VERB
iajs-1020	93	8	by	by	ADP
iajs-1020	93	9	the	the	DET
iajs-1020	93	10	following	follow	VERB
iajs-1020	93	11	example	example	NOUN
iajs-1020	93	12	;	;	PUNCT
iajs-1020	93	13	in	in	ADP
iajs-1020	93	14	projective	projective	ADJ
iajs-1020	93	15	plan	plan	PROPN
iajs-1020	93	16	pg(2,4	pg(2,4	PROPN
iajs-1020	93	17	)	)	PUNCT
iajs-1020	93	18	,	,	PUNCT
iajs-1020	93	19	let	let	VERB
iajs-1020	93	20	b	b	NOUN
iajs-1020	93	21	=	=	SYM
iajs-1020	93	22	{	{	PUNCT
iajs-1020	93	23	1,2,5,8,9,10,12,13,14,15,16,21	1,2,5,8,9,10,12,13,14,15,16,21	NOUN
iajs-1020	93	24	}	}	PUNCT
iajs-1020	93	25	,	,	PUNCT
iajs-1020	93	26	then	then	ADV
iajs-1020	93	27	b	b	PROPN
iajs-1020	93	28	is	be	AUX
iajs-1020	93	29	blocking	block	VERB
iajs-1020	93	30	set	set	NOUN
iajs-1020	93	31	but	but	CCONJ
iajs-1020	93	32	it	it	PRON
iajs-1020	93	33	is	be	AUX
iajs-1020	93	34	not	not	PART
iajs-1020	93	35	a	a	DET
iajs-1020	93	36	unital	unital	ADJ
iajs-1020	93	37	set	set	NOUN
iajs-1020	93	38	since	since	SCONJ
iajs-1020	93	39	:	:	PUNCT
iajs-1020	94	1	1	1	X
iajs-1020	94	2	.	.	X
iajs-1020	95	1	every	every	DET
iajs-1020	95	2	unital	unital	NOUN
iajs-1020	95	3	in	in	ADP
iajs-1020	95	4	pg(2,4	pg(2,4	NOUN
iajs-1020	95	5	)	)	PUNCT
iajs-1020	95	6	contains	contain	VERB
iajs-1020	95	7	(	(	PUNCT
iajs-1020	95	8	9	9	NUM
iajs-1020	95	9	)	)	PUNCT
iajs-1020	95	10	points	point	NOUN
iajs-1020	95	11	,	,	PUNCT
iajs-1020	95	12	but	but	CCONJ
iajs-1020	95	13	b	b	X
iajs-1020	95	14	contains	contain	NOUN
iajs-1020	95	15	(	(	PUNCT
iajs-1020	95	16	12	12	NUM
iajs-1020	95	17	)	)	PUNCT
iajs-1020	95	18	points	point	NOUN
iajs-1020	95	19	.	.	PUNCT
iajs-1020	96	1	2	2	X
iajs-1020	96	2	.	.	X
iajs-1020	96	3	some	some	DET
iajs-1020	96	4	line	line	NOUN
iajs-1020	96	5	in	in	ADP
iajs-1020	96	6	pg(2,4	pg(2,4	NOUN
iajs-1020	96	7	)	)	PUNCT
iajs-1020	96	8	meets	meet	VERB
iajs-1020	96	9	(	(	PUNCT
iajs-1020	96	10	k,4)-arc	k,4)-arc	X
iajs-1020	96	11	in	in	ADP
iajs-1020	96	12	4	4	NUM
iajs-1020	96	13	points	point	NOUN
iajs-1020	96	14	,	,	PUNCT
iajs-1020	96	15	but	but	CCONJ
iajs-1020	96	16	every	every	DET
iajs-1020	96	17	line	line	NOUN
iajs-1020	96	18	most	most	ADV
iajs-1020	96	19	meets	meet	VERB
iajs-1020	96	20	every	every	DET
iajs-1020	96	21	unital	unital	ADJ
iajs-1020	96	22	set	set	NOUN
iajs-1020	96	23	in	in	ADP
iajs-1020	96	24	either	either	PRON
iajs-1020	96	25	1	1	NUM
iajs-1020	96	26	or	or	CCONJ
iajs-1020	96	27	3	3	NUM
iajs-1020	96	28	points	point	NOUN
iajs-1020	96	29	.	.	PUNCT
iajs-1020	97	1	ihjpas	ihjpas	PROPN
iajs-1020	97	2	theorem	theorem	VERB
iajs-1020	97	3	let	let	VERB
iajs-1020	97	4	u	u	PRON
iajs-1020	97	5	be	be	AUX
iajs-1020	97	6	a	a	DET
iajs-1020	97	7	unital	unital	ADJ
iajs-1020	97	8	set	set	NOUN
iajs-1020	97	9	in	in	ADP
iajs-1020	97	10	pg(2,q2	pg(2,q2	PROPN
iajs-1020	97	11	)	)	PUNCT
iajs-1020	97	12	then	then	ADV
iajs-1020	97	13	every	every	DET
iajs-1020	97	14	point	point	NOUN
iajs-1020	97	15	p	p	X
iajs-1020	97	16			NOUN
iajs-1020	97	17	u	u	NOUN
iajs-1020	97	18	,	,	PUNCT
iajs-1020	97	19	p	p	NOUN
iajs-1020	97	20	is	be	AUX
iajs-1020	97	21	either	either	DET
iajs-1020	97	22	nucleus	nucleus	ADJ
iajs-1020	97	23	point	point	NOUN
iajs-1020	97	24	or	or	CCONJ
iajs-1020	97	25	(	(	PUNCT
iajs-1020	97	26	q+1)-fold	q+1)-fold	ADJ
iajs-1020	97	27	nucleus	nucleus	ADJ
iajs-1020	97	28	point	point	NOUN
iajs-1020	97	29	.	.	PUNCT
iajs-1020	98	1	proof	proof	NOUN
iajs-1020	98	2	:	:	PUNCT
iajs-1020	98	3	let	let	VERB
iajs-1020	98	4	u	u	PRON
iajs-1020	98	5	is	be	AUX
iajs-1020	98	6	a	a	DET
iajs-1020	98	7	unital	unital	ADJ
iajs-1020	98	8	set	set	NOUN
iajs-1020	98	9	,	,	PUNCT
iajs-1020	98	10	then	then	ADV
iajs-1020	98	11	every	every	DET
iajs-1020	98	12	line	line	NOUN
iajs-1020	98	13	meets	meet	VERB
iajs-1020	98	14	u	u	NOUN
iajs-1020	98	15	in	in	ADP
iajs-1020	98	16	either	either	PRON
iajs-1020	98	17	1	1	NUM
iajs-1020	98	18	or	or	CCONJ
iajs-1020	98	19	q	q	ADJ
iajs-1020	99	1	+	+	CCONJ
iajs-1020	99	2	1	1	NUM
iajs-1020	99	3	point	point	NOUN
iajs-1020	99	4	,	,	PUNCT
iajs-1020	99	5	for	for	ADP
iajs-1020	99	6	every	every	DET
iajs-1020	99	7	point	point	NOUN
iajs-1020	99	8	p	p	X
iajs-1020	99	9	,	,	PUNCT
iajs-1020	99	10	every	every	DET
iajs-1020	99	11	line	line	NOUN
iajs-1020	99	12	through	through	ADP
iajs-1020	99	13	p	p	PROPN
iajs-1020	99	14	meets	meet	VERB
iajs-1020	99	15	u	u	NOUN
iajs-1020	99	16	in	in	ADP
iajs-1020	99	17	either	either	DET
iajs-1020	99	18	1	1	NUM
iajs-1020	99	19	or	or	CCONJ
iajs-1020	99	20	q	q	ADJ
iajs-1020	99	21	+	+	CCONJ
iajs-1020	99	22	1	1	NUM
iajs-1020	99	23	points	point	NOUN
iajs-1020	99	24	,	,	PUNCT
iajs-1020	99	25	then	then	ADV
iajs-1020	99	26	p	p	NOUN
iajs-1020	99	27	is	be	AUX
iajs-1020	99	28	either	either	PRON
iajs-1020	99	29	nucleus	nucleus	NOUN
iajs-1020	99	30	or	or	CCONJ
iajs-1020	99	31	q	q	NOUN
iajs-1020	100	1	+	+	NOUN
iajs-1020	100	2	1	1	NUM
iajs-1020	100	3	-	-	ADJ
iajs-1020	100	4	fold	fold	ADJ
iajs-1020	100	5	nucleus	nucleus	ADJ
iajs-1020	100	6	point	point	NOUN
iajs-1020	100	7	.	.	PUNCT
iajs-1020	101	1	theorem	theorem	VERB
iajs-1020	101	2	let	let	VERB
iajs-1020	101	3	s	s	PRON
iajs-1020	101	4	=	=	VERB
iajs-1020	101	5	{	{	PUNCT
iajs-1020	101	6	(	(	PUNCT
iajs-1020	101	7	p	p	X
iajs-1020	101	8	i	i	PROPN
iajs-1020	101	9	,	,	PUNCT
iajs-1020	101	10	li	li	PROPN
iajs-1020	101	11	)	)	PUNCT
iajs-1020	101	12	;	;	PUNCT
iajs-1020	101	13	pi	pi	PROPN
iajs-1020	101	14			PROPN
iajs-1020	101	15	b	b	PROPN
iajs-1020	101	16	,	,	PUNCT
iajs-1020	101	17	b	b	PROPN
iajs-1020	101	18	is	be	AUX
iajs-1020	101	19	minimal	minimal	ADJ
iajs-1020	101	20	blocking	blocking	NOUN
iajs-1020	101	21	set	set	NOUN
iajs-1020	101	22	;	;	PUNCT
iajs-1020	101	23	li	li	PROPN
iajs-1020	101	24	pg(2,q	pg(2,q	PROPN
iajs-1020	101	25	)	)	PUNCT
iajs-1020	101	26	i	i	PROPN
iajs-1020	101	27	}	}	PUNCT
iajs-1020	101	28	then	then	ADV
iajs-1020	101	29	s	s	VERB
iajs-1020	101	30	is	be	AUX
iajs-1020	101	31	a	a	DET
iajs-1020	101	32	strong	strong	ADJ
iajs-1020	101	33	representive	representive	ADJ
iajs-1020	101	34	system	system	NOUN
iajs-1020	101	35	.	.	PUNCT
iajs-1020	102	1	proof	proof	NOUN
iajs-1020	102	2	:	:	PUNCT
iajs-1020	102	3	let	let	VERB
iajs-1020	102	4	s	s	PRON
iajs-1020	102	5	=	=	VERB
iajs-1020	102	6	{	{	PUNCT
iajs-1020	102	7	(	(	PUNCT
iajs-1020	102	8	p	p	X
iajs-1020	102	9	i	i	PROPN
iajs-1020	102	10	,	,	PUNCT
iajs-1020	102	11	lj	lj	PROPN
iajs-1020	102	12	)	)	PUNCT
iajs-1020	102	13	;	;	PUNCT
iajs-1020	102	14	pi	pi	PROPN
iajs-1020	102	15			PROPN
iajs-1020	102	16	b	b	PROPN
iajs-1020	102	17	,	,	PUNCT
iajs-1020	102	18			NOUN
iajs-1020	102	19	i	i	PRON
iajs-1020	102	20	;	;	PUNCT
iajs-1020	102	21	lj	lj	PROPN
iajs-1020	102	22			NOUN
iajs-1020	102	23	pg(2,q	pg(2,q	NOUN
iajs-1020	102	24	)	)	PUNCT
iajs-1020	102	25	}	}	PUNCT
iajs-1020	102	26	to	to	PART
iajs-1020	102	27	prove	prove	VERB
iajs-1020	102	28	that	that	SCONJ
iajs-1020	102	29	s	s	VERB
iajs-1020	102	30	is	be	AUX
iajs-1020	102	31	a	a	DET
iajs-1020	102	32	strong	strong	ADJ
iajs-1020	102	33	representive	representive	ADJ
iajs-1020	102	34	system	system	NOUN
iajs-1020	102	35	.	.	PUNCT
iajs-1020	103	1	suppose	suppose	VERB
iajs-1020	103	2	that	that	SCONJ
iajs-1020	103	3	s	s	VERB
iajs-1020	103	4	is	be	AUX
iajs-1020	103	5	not	not	PART
iajs-1020	103	6	strong	strong	ADJ
iajs-1020	103	7	representive	representive	ADJ
iajs-1020	103	8	system	system	NOUN
iajs-1020	103	9	then	then	ADV
iajs-1020	103	10			PROPN
iajs-1020	103	11	p0,p1	p0,p1	PROPN
iajs-1020	103	12			NOUN
iajs-1020	103	13	b	b	PROPN
iajs-1020	103	14	s.t	s.t	PROPN
iajs-1020	103	15	.	.	PUNCT
iajs-1020	104	1			NUM
iajs-1020	104	2	l	l	NOUN
iajs-1020	104	3			NOUN
iajs-1020	104	4	pg(2,q	pg(2,q	VERB
iajs-1020	104	5	)	)	PUNCT
iajs-1020	104	6	such	such	ADJ
iajs-1020	104	7	that	that	SCONJ
iajs-1020	104	8	(	(	PUNCT
iajs-1020	104	9	p0,l	p0,l	PROPN
iajs-1020	104	10	)	)	PUNCT
iajs-1020	104	11	,	,	PUNCT
iajs-1020	104	12	(	(	PUNCT
iajs-1020	104	13	p1,l	p1,l	PROPN
iajs-1020	104	14	)	)	PUNCT
iajs-1020	104	15			NOUN
iajs-1020	104	16	s	s	PROPN
iajs-1020	104	17	,	,	PUNCT
iajs-1020	104	18	then	then	ADV
iajs-1020	104	19	the	the	DET
iajs-1020	104	20	line	line	NOUN
iajs-1020	104	21	l	l	NOUN
iajs-1020	104	22	in	in	ADP
iajs-1020	104	23	pg(2,q	pg(2,q	PRON
iajs-1020	104	24	)	)	PUNCT
iajs-1020	104	25	intersects	intersect	NOUN
iajs-1020	104	26	b	b	NOUN
iajs-1020	104	27	in	in	ADP
iajs-1020	104	28	p0	p0	NOUN
iajs-1020	104	29	,	,	PUNCT
iajs-1020	104	30	p1	p1	PROPN
iajs-1020	104	31			NOUN
iajs-1020	104	32	b	b	X
iajs-1020	104	33	\	\	PROPN
iajs-1020	104	34	{	{	PUNCT
iajs-1020	104	35	p0	p0	NOUN
iajs-1020	104	36	}	}	PUNCT
iajs-1020	104	37	or	or	CCONJ
iajs-1020	104	38	b	b	NOUN
iajs-1020	104	39	\{p1	\{p1	X
iajs-1020	104	40	}	}	PUNCT
iajs-1020	104	41	is	be	AUX
iajs-1020	104	42	blocking	block	VERB
iajs-1020	104	43	set	set	NOUN
iajs-1020	104	44	,	,	PUNCT
iajs-1020	104	45	which	which	PRON
iajs-1020	104	46	is	be	AUX
iajs-1020	104	47	contradiction	contradiction	NOUN
iajs-1020	104	48	since	since	SCONJ
iajs-1020	104	49	b	b	NOUN
iajs-1020	104	50	is	be	AUX
iajs-1020	104	51	a	a	DET
iajs-1020	104	52	minimal	minimal	ADJ
iajs-1020	104	53	blocking	blocking	NOUN
iajs-1020	104	54	set	set	NOUN
iajs-1020	104	55	and	and	CCONJ
iajs-1020	104	56			NOUN
iajs-1020	104	57	l	l	PROPN
iajs-1020	104	58			PROPN
iajs-1020	104	59	pg(2,q	pg(2,q	VERB
iajs-1020	104	60	)	)	PUNCT
iajs-1020	104	61	,	,	PUNCT
iajs-1020	104	62	l	l	X
iajs-1020	104	63			NOUN
iajs-1020	104	64	b	b	NUM
iajs-1020	104	65	=	=	SYM
iajs-1020	104	66	p	p	NOUN
iajs-1020	104	67	or	or	CCONJ
iajs-1020	104	68	l	l	NOUN
iajs-1020	104	69	is	be	AUX
iajs-1020	104	70	tangent	tangent	ADJ
iajs-1020	104	71	to	to	ADP
iajs-1020	104	72	b	b	NOUN
iajs-1020	104	73	in	in	ADP
iajs-1020	104	74	p.	p.	NOUN
iajs-1020	104	75	theorem	theorem	VERB
iajs-1020	104	76	every	every	PRON
iajs-1020	104	77	maximal	maximal	ADJ
iajs-1020	104	78	(	(	PUNCT
iajs-1020	104	79	k,2)-arc	k,2)-arc	NOUN
iajs-1020	104	80	in	in	ADP
iajs-1020	104	81	pg(2,q	pg(2,q	NOUN
iajs-1020	104	82	)	)	PUNCT
iajs-1020	104	83	with	with	ADP
iajs-1020	104	84	no	no	DET
iajs-1020	104	85	0	0	NUM
iajs-1020	104	86	-	-	PUNCT
iajs-1020	104	87	secant	secant	NOUN
iajs-1020	104	88	is	be	AUX
iajs-1020	104	89	a	a	DET
iajs-1020	104	90	set	set	NOUN
iajs-1020	104	91	of	of	ADP
iajs-1020	104	92	type	type	NOUN
iajs-1020	104	93	(	(	PUNCT
iajs-1020	104	94	0,1,2,q+1)-set	0,1,2,q+1)-set	NOUN
iajs-1020	104	95	.	.	PUNCT
iajs-1020	105	1	proof	proof	NOUN
iajs-1020	105	2	:	:	PUNCT
iajs-1020	105	3	it	it	PRON
iajs-1020	105	4	is	be	AUX
iajs-1020	105	5	clear	clear	ADJ
iajs-1020	105	6	that	that	SCONJ
iajs-1020	105	7	the	the	DET
iajs-1020	105	8	maximal	maximal	ADJ
iajs-1020	105	9	(	(	PUNCT
iajs-1020	105	10	k,2)-arc	k,2)-arc	NOUN
iajs-1020	105	11	with	with	ADP
iajs-1020	105	12	no	no	DET
iajs-1020	105	13	0	0	NUM
iajs-1020	105	14	-	-	PUNCT
iajs-1020	105	15	secant	secant	ADJ
iajs-1020	105	16	mean	mean	NOUN
iajs-1020	105	17	that	that	SCONJ
iajs-1020	105	18	every	every	DET
iajs-1020	105	19	line	line	NOUN
iajs-1020	105	20	in	in	ADP
iajs-1020	105	21	pg(2,q	pg(2,q	NOUN
iajs-1020	105	22	)	)	PUNCT
iajs-1020	105	23	is	be	AUX
iajs-1020	105	24	a	a	DET
iajs-1020	105	25	2secant	2secant	NUM
iajs-1020	105	26	of	of	ADP
iajs-1020	105	27	(	(	PUNCT
iajs-1020	105	28	k,2)-arc	k,2)-arc	NOUN
iajs-1020	105	29	,	,	PUNCT
iajs-1020	105	30	so	so	CCONJ
iajs-1020	105	31	every	every	DET
iajs-1020	105	32	line	line	NOUN
iajs-1020	105	33	intersects	intersect	NOUN
iajs-1020	105	34	maximal	maximal	ADJ
iajs-1020	105	35	(	(	PUNCT
iajs-1020	105	36	k,2)-arc	k,2)-arc	NOUN
iajs-1020	105	37	in	in	ADP
iajs-1020	105	38	two	two	NUM
iajs-1020	105	39	points	point	NOUN
iajs-1020	105	40	then	then	ADV
iajs-1020	105	41	the	the	DET
iajs-1020	105	42	maximal	maximal	ADJ
iajs-1020	105	43	(	(	PUNCT
iajs-1020	105	44	k,2)-arc	k,2)-arc	PROPN
iajs-1020	105	45	is	be	AUX
iajs-1020	105	46	a	a	DET
iajs-1020	105	47	set	set	NOUN
iajs-1020	105	48	of	of	ADP
iajs-1020	105	49	type	type	NOUN
iajs-1020	105	50	(	(	PUNCT
iajs-1020	105	51	0,1,2,q+1)-set	0,1,2,q+1)-set	NOUN
iajs-1020	105	52	.	.	PUNCT
iajs-1020	106	1	4	4	X
iajs-1020	106	2	.	.	X
iajs-1020	106	3	conclusion	conclusion	NOUN
iajs-1020	106	4	and	and	CCONJ
iajs-1020	106	5	recommandation	recommandation	NOUN
iajs-1020	106	6	in	in	ADP
iajs-1020	106	7	this	this	DET
iajs-1020	106	8	research	research	NOUN
iajs-1020	106	9	,	,	PUNCT
iajs-1020	106	10	we	we	PRON
iajs-1020	106	11	took	take	VERB
iajs-1020	106	12	of	of	ADP
iajs-1020	106	13	subspaces	subspace	NOUN
iajs-1020	106	14	of	of	ADP
iajs-1020	106	15	pg(2,q	pg(2,q	NOUN
iajs-1020	106	16	)	)	PUNCT
iajs-1020	106	17	like	like	ADP
iajs-1020	106	18	blocking	block	VERB
iajs-1020	106	19	,	,	PUNCT
iajs-1020	106	20	nuclei	nucleus	NOUN
iajs-1020	106	21	,	,	PUNCT
iajs-1020	106	22	unital	unital	ADJ
iajs-1020	106	23	,	,	PUNCT
iajs-1020	106	24	(	(	PUNCT
iajs-1020	106	25	0,1,2,q+1	0,1,2,q+1	NUM
iajs-1020	106	26	)	)	PUNCT
iajs-1020	106	27	–	–	PUNCT
iajs-1020	106	28	set	set	VERB
iajs-1020	106	29	,	,	PUNCT
iajs-1020	106	30	strong	strong	ADJ
iajs-1020	106	31	representive	representive	ADJ
iajs-1020	106	32	system	system	NOUN
iajs-1020	106	33	and	and	CCONJ
iajs-1020	106	34	complete	complete	ADJ
iajs-1020	106	35	nuclei	nucleus	NOUN
iajs-1020	106	36	set	set	VERB
iajs-1020	106	37	as	as	ADP
iajs-1020	106	38	new	new	ADJ
iajs-1020	106	39	definitions	definition	NOUN
iajs-1020	106	40	.	.	PUNCT
iajs-1020	107	1	then	then	ADV
iajs-1020	107	2	we	we	PRON
iajs-1020	107	3	found	find	VERB
iajs-1020	107	4	some	some	DET
iajs-1020	107	5	relations	relation	NOUN
iajs-1020	107	6	between	between	ADP
iajs-1020	107	7	these	these	DET
iajs-1020	107	8	subsets	subset	NOUN
iajs-1020	107	9	and	and	CCONJ
iajs-1020	107	10	explain	explain	VERB
iajs-1020	107	11	them	they	PRON
iajs-1020	107	12	by	by	ADP
iajs-1020	107	13	theorems	theorem	NOUN
iajs-1020	107	14	like	like	ADP
iajs-1020	107	15	;	;	PUNCT
iajs-1020	107	16	if	if	SCONJ
iajs-1020	107	17	n(s	n(	NOUN
iajs-1020	107	18	)	)	PUNCT
iajs-1020	107	19	is	be	AUX
iajs-1020	107	20	complete	complete	ADJ
iajs-1020	108	1	then	then	ADV
iajs-1020	108	2	s	s	VERB
iajs-1020	108	3	is	be	AUX
iajs-1020	108	4	line	line	NOUN
iajs-1020	108	5	,	,	PUNCT
iajs-1020	108	6			NOUN
iajs-1020	108	7	p	p	PROPN
iajs-1020	108	8			PROPN
iajs-1020	108	9	pg(2,q)\b	pg(2,q)\b	NOUN
iajs-1020	108	10	,	,	PUNCT
iajs-1020	108	11	p	p	PROPN
iajs-1020	108	12	is	be	AUX
iajs-1020	108	13	t	t	NOUN
iajs-1020	108	14	-	-	ADJ
iajs-1020	108	15	fold	fold	ADJ
iajs-1020	108	16	nucleus	nucleus	NOUN
iajs-1020	108	17	,	,	PUNCT
iajs-1020	108	18	if	if	SCONJ
iajs-1020	108	19	and	and	CCONJ
iajs-1020	108	20	only	only	ADV
iajs-1020	108	21	if	if	SCONJ
iajs-1020	108	22	b	b	PROPN
iajs-1020	108	23	is	be	AUX
iajs-1020	108	24	t	t	NOUN
iajs-1020	108	25	-	-	PUNCT
iajs-1020	108	26	fold	fold	ADJ
iajs-1020	108	27	blocking	blocking	NOUN
iajs-1020	108	28	set	set	NOUN
iajs-1020	108	29	,	,	PUNCT
iajs-1020	108	30	every	every	DET
iajs-1020	108	31	unital	unital	ADJ
iajs-1020	108	32	set	set	NOUN
iajs-1020	108	33	is	be	AUX
iajs-1020	108	34	(	(	PUNCT
iajs-1020	108	35	qp+1,p+1)-arc	qp+1,p+1)-arc	NOUN
iajs-1020	108	36	,	,	PUNCT
iajs-1020	108	37	q	q	X
iajs-1020	108	38			NUM
iajs-1020	108	39	3	3	NUM
iajs-1020	108	40	,	,	PUNCT
iajs-1020	108	41	pu	pu	ADV
iajs-1020	108	42	,	,	PUNCT
iajs-1020	108	43	u	u	NOUN
iajs-1020	108	44	is	be	AUX
iajs-1020	108	45	unital	unital	ADJ
iajs-1020	108	46	set	set	NOUN
iajs-1020	108	47	then	then	ADV
iajs-1020	108	48	p	p	NOUN
iajs-1020	108	49	is	be	AUX
iajs-1020	108	50	either	either	CCONJ
iajs-1020	108	51	nucleus	nucleus	NOUN
iajs-1020	108	52	or	or	CCONJ
iajs-1020	108	53	q+1fold	q+1fold	VERB
iajs-1020	108	54	nucleus	nucleus	NOUN
iajs-1020	108	55	point	point	NOUN
iajs-1020	108	56	and	and	CCONJ
iajs-1020	108	57	other	other	ADJ
iajs-1020	108	58	relations	relation	NOUN
iajs-1020	108	59	.	.	PUNCT
iajs-1020	109	1	some	some	PRON
iajs-1020	109	2	of	of	ADP
iajs-1020	109	3	definitions	definition	NOUN
iajs-1020	109	4	were	be	AUX
iajs-1020	109	5	explained	explain	VERB
iajs-1020	109	6	by	by	ADP
iajs-1020	109	7	examples	example	NOUN
iajs-1020	109	8	and	and	CCONJ
iajs-1020	109	9	tables	table	NOUN
iajs-1020	109	10	like	like	ADP
iajs-1020	109	11	unital	unital	ADJ
iajs-1020	109	12	set	set	NOUN
iajs-1020	109	13	and	and	CCONJ
iajs-1020	109	14	nucleus	nucleus	ADJ
iajs-1020	109	15	point	point	NOUN
iajs-1020	109	16	.	.	PUNCT
iajs-1020	110	1	so	so	ADV
iajs-1020	110	2	as	as	ADP
iajs-1020	110	3	some	some	DET
iajs-1020	110	4	theorems	theorem	NOUN
iajs-1020	110	5	,	,	PUNCT
iajs-1020	110	6	this	this	DET
iajs-1020	110	7	relation	relation	NOUN
iajs-1020	110	8	will	will	AUX
iajs-1020	110	9	lead	lead	VERB
iajs-1020	110	10	to	to	PART
iajs-1020	110	11	make	make	VERB
iajs-1020	110	12	new	new	ADJ
iajs-1020	110	13	sets	set	NOUN
iajs-1020	110	14	of	of	ADP
iajs-1020	110	15	subspaces	subspace	NOUN
iajs-1020	110	16	included	include	VERB
iajs-1020	110	17	at	at	ADP
iajs-1020	110	18	this	this	DET
iajs-1020	110	19	projective	projective	ADJ
iajs-1020	110	20	space	space	NOUN
iajs-1020	110	21	or	or	CCONJ
iajs-1020	110	22	others	other	NOUN
iajs-1020	110	23	.	.	PUNCT
iajs-1020	111	1	references	reference	NOUN
iajs-1020	111	2	1	1	NUM
iajs-1020	111	3	.	.	X
iajs-1020	111	4	susan	susan	PROPN
iajs-1020	111	5	barwich	barwich	PROPN
iajs-1020	111	6	,	,	PUNCT
iajs-1020	111	7	and	and	CCONJ
iajs-1020	111	8	gary	gary	PROPN
iajs-1020	111	9	ebert	ebert	PROPN
iajs-1020	111	10	,	,	PUNCT
iajs-1020	111	11	(	(	PUNCT
iajs-1020	111	12	2008	2008	NUM
iajs-1020	111	13	)	)	PUNCT
iajs-1020	111	14	.	.	PUNCT
iajs-1020	112	1	"	"	PUNCT
iajs-1020	112	2	unitals	unital	NOUN
iajs-1020	112	3	in	in	ADP
iajs-1020	112	4	projective	projective	ADJ
iajs-1020	112	5	plane	plane	NOUN
iajs-1020	112	6	"	"	PUNCT
iajs-1020	112	7	,	,	PUNCT
iajs-1020	112	8	doi:10.1007/9780	doi:10.1007/9780	NOUN
iajs-1020	112	9	-	-	SYM
iajs-1020	112	10	387	387	NUM
iajs-1020	112	11	-	-	NUM
iajs-1020	112	12	76366	76366	NUM
iajs-1020	112	13	-	-	PUNCT
iajs-1020	112	14	8	8	NUM
iajs-1020	112	15	-	-	SYM
iajs-1020	112	16	1	1	NUM
iajs-1020	112	17	,	,	PUNCT
iajs-1020	112	18	©	©	PROPN
iajs-1020	112	19	springer	springer	NOUN
iajs-1020	112	20	science	science	NOUN
iajs-1020	112	21	+	+	CCONJ
iajs-1020	112	22	business	business	NOUN
iajs-1020	112	23	media	medium	NOUN
iajs-1020	112	24	,	,	PUNCT
iajs-1020	112	25	llc	llc	PROPN
iajs-1020	112	26	2	2	NUM
iajs-1020	112	27	.	.	PUNCT
iajs-1020	112	28	blokhuis	blokhuis	PROPN
iajs-1020	112	29	,	,	PUNCT
iajs-1020	112	30	a.	a.	NOUN
iajs-1020	112	31	;	;	PUNCT
iajs-1020	112	32	hischfed	hischfe	VERB
iajs-1020	112	33	,	,	PUNCT
iajs-1020	112	34	j.w.p	j.w.p	NOUN
iajs-1020	112	35	.	.	PUNCT
iajs-1020	113	1	;	;	PUNCT
iajs-1020	113	2	jungnickd.and	jungnickd.and	PROPN
iajs-1020	113	3	thas	thas	PROPN
iajs-1020	113	4	,	,	PUNCT
iajs-1020	113	5	j	j	PROPN
iajs-1020	113	6	.f	.f	PROPN
iajs-1020	113	7	.	.	PUNCT
iajs-1020	114	1	(	(	PUNCT
iajs-1020	114	2	2001	2001	NUM
iajs-1020	114	3	)	)	PUNCT
iajs-1020	114	4	,	,	PUNCT
iajs-1020	114	5	"	"	PUNCT
iajs-1020	114	6	finite	finite	PROPN
iajs-1020	114	7	geometries	geometry	NOUN
iajs-1020	114	8	"	"	PUNCT
iajs-1020	114	9	,	,	PUNCT
iajs-1020	114	10	kluwer	kluwer	NOUN
iajs-1020	114	11	academic	academic	NOUN
iajs-1020	114	12	,	,	PUNCT
iajs-1020	114	13	publishers	publisher	NOUN
iajs-1020	114	14	.	.	PUNCT
iajs-1020	115	1	3	3	X
iajs-1020	115	2	.	.	X
iajs-1020	115	3	beutel	beutel	PROPN
iajs-1020	115	4	spacher	spacher	PROPN
iajs-1020	115	5	,	,	PUNCT
iajs-1020	115	6	a.and	a.and	CCONJ
iajs-1020	115	7	de	de	X
iajs-1020	115	8	clerck	clerck	PROPN
iajs-1020	115	9	,	,	PUNCT
iajs-1020	115	10	f.	f.	PROPN
iajs-1020	115	11	(	(	PUNCT
iajs-1020	115	12	1993	1993	NUM
iajs-1020	115	13	)	)	PUNCT
iajs-1020	115	14	,	,	PUNCT
iajs-1020	115	15	"	"	PUNCT
iajs-1020	115	16	finite	finite	ADJ
iajs-1020	115	17	geometry	geometry	NOUN
iajs-1020	115	18	and	and	CCONJ
iajs-1020	115	19	combinatorics	combinatoric	NOUN
iajs-1020	115	20	"	"	PUNCT
iajs-1020	115	21	,	,	PUNCT
iajs-1020	115	22	combridge	combridge	PROPN
iajs-1020	115	23	university	university	NOUN
iajs-1020	115	24	press	press	NOUN
iajs-1020	115	25	.	.	PUNCT
iajs-1020	116	1	4	4	X
iajs-1020	116	2	.	.	X
iajs-1020	116	3	lamb	lamb	PROPN
iajs-1020	116	4	,	,	PUNCT
iajs-1020	116	5	j.d.and	j.d.and	PROPN
iajs-1020	116	6	preece	preece	PROPN
iajs-1020	116	7	,	,	PUNCT
iajs-1020	116	8	d.a	d.a	PROPN
iajs-1020	116	9	.	.	PROPN
iajs-1020	116	10	(	(	PUNCT
iajs-1020	116	11	1999	1999	NUM
iajs-1020	116	12	)	)	PUNCT
iajs-1020	116	13	,	,	PUNCT
iajs-1020	116	14	"	"	PUNCT
iajs-1020	116	15	surreys	surrey	NOUN
iajs-1020	116	16	in	in	ADP
iajs-1020	116	17	combinatorics	combinatoric	NOUN
iajs-1020	116	18	"	"	PUNCT
iajs-1020	116	19	,	,	PUNCT
iajs-1020	116	20	combridge	combridge	PROPN
iajs-1020	116	21	university	university	NOUN
iajs-1020	116	22	press	press	NOUN
iajs-1020	116	23	.	.	PUNCT
iajs-1020	117	1	ihjpas	ihjpas	PROPN
iajs-1020	117	2	table	table	NOUN
iajs-1020	117	3	(	(	PUNCT
iajs-1020	117	4	1.1):the	1.1):the	DET
iajs-1020	117	5	points	point	NOUN
iajs-1020	117	6	and	and	CCONJ
iajs-1020	117	7	lines	line	NOUN
iajs-1020	117	8	of	of	ADP
iajs-1020	117	9	pg(2,4	pg(2,4	NOUN
iajs-1020	117	10	)	)	PUNCT
iajs-1020	117	11	table	table	NOUN
iajs-1020	117	12	(	(	PUNCT
iajs-1020	117	13	1.2	1.2	NUM
iajs-1020	117	14	)	)	PUNCT
iajs-1020	117	15	:	:	PUNCT
iajs-1020	117	16	the	the	DET
iajs-1020	117	17	points	point	NOUN
iajs-1020	117	18	and	and	CCONJ
iajs-1020	117	19	lines	line	NOUN
iajs-1020	117	20	of	of	ADP
iajs-1020	117	21	untial	untial	ADJ
iajs-1020	117	22	set	set	NOUN
iajs-1020	118	1	i	i	PRON
iajs-1020	118	2	pi	pi	NOUN
iajs-1020	118	3	li	li	PROPN
iajs-1020	118	4	1	1	NUM
iajs-1020	119	1	1	1	NUM
iajs-1020	119	2	0	0	NUM
iajs-1020	119	3	0	0	NUM
iajs-1020	119	4	1	1	NUM
iajs-1020	119	5	2	2	NUM
iajs-1020	119	6	3	3	NUM
iajs-1020	119	7	4	4	NUM
iajs-1020	119	8	5	5	NUM
iajs-1020	119	9	2	2	NUM
iajs-1020	119	10	0	0	NUM
iajs-1020	119	11	1	1	NUM
iajs-1020	119	12	0	0	NUM
iajs-1020	119	13	2	2	NUM
iajs-1020	119	14	6	6	NUM
iajs-1020	119	15	10	10	NUM
iajs-1020	119	16	14	14	NUM
iajs-1020	119	17	18	18	NUM
iajs-1020	119	18	3	3	NUM
iajs-1020	119	19	1	1	NUM
iajs-1020	119	20	1	1	NUM
iajs-1020	119	21	0	0	NUM
iajs-1020	119	22	4	4	NUM
iajs-1020	119	23	6	6	NUM
iajs-1020	119	24	12	12	NUM
iajs-1020	119	25	17	17	NUM
iajs-1020	119	26	19	19	NUM
iajs-1020	119	27	4	4	NUM
iajs-1020	119	28	2	2	NUM
iajs-1020	119	29	1	1	NUM
iajs-1020	119	30	0	0	NUM
iajs-1020	119	31	5	5	NUM
iajs-1020	119	32	7	7	NUM
iajs-1020	119	33	12	12	NUM
iajs-1020	119	34	14	14	NUM
iajs-1020	119	35	21	21	NUM
iajs-1020	119	36	5	5	NUM
iajs-1020	119	37	3	3	NUM
iajs-1020	119	38	1	1	NUM
iajs-1020	119	39	0	0	NUM
iajs-1020	119	40	5	5	NUM
iajs-1020	119	41	8	8	NUM
iajs-1020	119	42	11	11	NUM
iajs-1020	119	43	17	17	NUM
iajs-1020	119	44	18	18	NUM
iajs-1020	119	45	6	6	NUM
iajs-1020	119	46	0	0	NUM
iajs-1020	119	47	0	0	NUM
iajs-1020	119	48	1	1	NUM
iajs-1020	119	49	1	1	NUM
iajs-1020	119	50	18	18	NUM
iajs-1020	119	51	19	19	NUM
iajs-1020	119	52	20	20	NUM
iajs-1020	119	53	21	21	NUM
iajs-1020	119	54	7	7	NUM
iajs-1020	119	55	1	1	NUM
iajs-1020	119	56	0	0	NUM
iajs-1020	119	57	1	1	NUM
iajs-1020	119	58	2	2	NUM
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iajs-1020	119	61	15	15	NUM
iajs-1020	119	62	19	19	NUM
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iajs-1020	119	66	1	1	NUM
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iajs-1020	119	77	8	8	NUM
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iajs-1020	119	84	1	1	NUM
iajs-1020	119	85	5	5	NUM
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iajs-1020	119	89	20	20	NUM
iajs-1020	119	90	11	11	NUM
iajs-1020	119	91	1	1	NUM
iajs-1020	119	92	1	1	NUM
iajs-1020	119	93	1	1	NUM
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iajs-1020	119	97	15	15	NUM
iajs-1020	119	98	18	18	NUM
iajs-1020	119	99	12	12	NUM
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iajs-1020	119	101	1	1	NUM
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iajs-1020	119	109	3	3	NUM
iajs-1020	119	110	1	1	NUM
iajs-1020	119	111	1	1	NUM
iajs-1020	119	112	4	4	NUM
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iajs-1020	119	115	16	16	NUM
iajs-1020	119	116	18	18	NUM
iajs-1020	119	117	14	14	NUM
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iajs-1020	119	119	2	2	NUM
iajs-1020	119	120	1	1	NUM
iajs-1020	119	121	3	3	NUM
iajs-1020	119	122	8	8	NUM
iajs-1020	119	123	13	13	NUM
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iajs-1020	119	125	19	19	NUM
iajs-1020	119	126	15	15	NUM
iajs-1020	119	127	1	1	NUM
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iajs-1020	119	129	1	1	NUM
iajs-1020	119	130	3	3	NUM
iajs-1020	119	131	7	7	NUM
iajs-1020	119	132	10	10	NUM
iajs-1020	119	133	17	17	NUM
iajs-1020	119	134	20	20	NUM
iajs-1020	119	135	16	16	NUM
iajs-1020	119	136	2	2	NUM
iajs-1020	119	137	2	2	NUM
iajs-1020	119	138	1	1	NUM
iajs-1020	119	139	4	4	NUM
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iajs-1020	119	143	21	21	NUM
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iajs-1020	119	145	3	3	NUM
iajs-1020	119	146	2	2	NUM
iajs-1020	119	147	1	1	NUM
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iajs-1020	119	152	20	20	NUM
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iajs-1020	119	155	3	3	NUM
iajs-1020	119	156	1	1	NUM
iajs-1020	119	157	1	1	NUM
iajs-1020	119	158	14	14	NUM
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iajs-1020	119	164	3	3	NUM
iajs-1020	119	165	1	1	NUM
iajs-1020	119	166	2	2	NUM
iajs-1020	119	167	9	9	NUM
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iajs-1020	119	169	17	17	NUM
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iajs-1020	119	171	20	20	NUM
iajs-1020	119	172	2	2	NUM
iajs-1020	119	173	3	3	NUM
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iajs-1020	119	182	3	3	NUM
iajs-1020	119	183	1	1	NUM
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iajs-1020	119	189	i	i	PRON
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iajs-1020	119	191	li	li	PROPN
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iajs-1020	119	205	1	1	NUM
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iajs-1020	119	210	19	19	NUM
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iajs-1020	119	218	1	1	NUM
iajs-1020	119	219	0	0	NUM
iajs-1020	119	220	11	11	NUM
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iajs-1020	119	225	0	0	NUM
iajs-1020	119	226	1	1	NUM
iajs-1020	119	227	1	1	NUM
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iajs-1020	119	229	19	19	NUM
iajs-1020	119	230	7	7	NUM
iajs-1020	119	231	1	1	NUM
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iajs-1020	119	233	1	1	NUM
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iajs-1020	119	255	1	1	NUM
iajs-1020	119	256	1	1	NUM
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iajs-1020	119	261	1	1	NUM
iajs-1020	119	262	1	1	NUM
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iajs-1020	119	268	1	1	NUM
iajs-1020	119	269	1	1	NUM
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iajs-1020	119	275	2	2	NUM
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iajs-1020	119	279	1	1	NUM
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iajs-1020	119	285	16	16	NUM
iajs-1020	119	286	2	2	NUM
iajs-1020	119	287	2	2	NUM
iajs-1020	119	288	1	1	NUM
iajs-1020	119	289	10	10	NUM
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iajs-1020	119	291	3	3	NUM
iajs-1020	119	292	2	2	NUM
iajs-1020	119	293	1	1	NUM
iajs-1020	119	294	11	11	NUM
iajs-1020	119	295	18	18	NUM
iajs-1020	119	296	0	0	NUM
iajs-1020	119	297	3	3	NUM
iajs-1020	119	298	1	1	NUM
iajs-1020	119	299	1	1	NUM
iajs-1020	119	300	16	16	NUM
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iajs-1020	119	302	19	19	NUM
iajs-1020	119	303	1	1	NUM
iajs-1020	119	304	3	3	NUM
iajs-1020	119	305	1	1	NUM
iajs-1020	119	306	17	17	NUM
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iajs-1020	119	309	3	3	NUM
iajs-1020	119	310	1	1	NUM
iajs-1020	119	311	6	6	NUM
iajs-1020	119	312	11	11	NUM
iajs-1020	119	313	16	16	NUM
iajs-1020	119	314	21	21	NUM
iajs-1020	119	315	3	3	NUM
iajs-1020	119	316	3	3	NUM
iajs-1020	119	317	1	1	NUM
iajs-1020	119	318	1	1	NUM
iajs-1020	119	319	10	10	NUM
iajs-1020	119	320	11	11	NUM
iajs-1020	119	321	ihjpas	ihjpa	NOUN
iajs-1020	119	322	graph	graph	NOUN
iajs-1020	119	323	:	:	PUNCT
iajs-1020	119	324	this	this	DET
iajs-1020	119	325	graph	graph	NOUN
iajs-1020	119	326	shows	show	VERB
iajs-1020	119	327	that	that	SCONJ
iajs-1020	119	328	a	a	DET
iajs-1020	119	329	set	set	NOUN
iajs-1020	119	330	s	s	NOUN
iajs-1020	119	331	contains	contain	VERB
iajs-1020	119	332	exactly	exactly	ADV
iajs-1020	119	333	q+1	q+1	NUM
iajs-1020	119	334	points	point	NOUN
iajs-1020	119	335	ihjpas	ihjpa	VERB