theorem
  ex q,r st not p,q,r are_collinear
proof
  consider q such that
A1: p<>q and
  p<>q and
  p,p,q are_collinear by ANPROJ_2:def 10;
  ex r st not p,q,r are_collinear by A1,Th4;
  hence thesis;
end;
