theorem Th9: :: ANPROJ_8:10

for V being non trivial RealLinearSpace
for p, q, r being Element of (ProjectiveSpace V) holds
( p,q,r are_collinear iff ex u, v, w being Element of V st
( p = Dir u & q = Dir v & r = Dir w & not u is zero & not v is zero & not w is zero & ( u = v or u = w or v = w or {u,v,w} is linearly-dependent ) ) )