reserve X for set;
reserve CS for non empty CollStr;
reserve a,b,c for Point of CS;
reserve CLSP for CollSp;
reserve a,b,c,d,p,q,r for Point of CLSP;
reserve i,j,k for Element of NAT;
reserve CLSP for proper CollSp;
reserve a,b,c,p,q,r for Point of CLSP;

theorem Th12:
  for p,q holds p<>q implies ex r st not p,q,r are_collinear
proof
  let p,q;
  consider a,b,c such that
A1: not a,b,c are_collinear by Def6;
  assume p<>q;
  then not p,q,a are_collinear or not p,q,b are_collinear or not p,q,c
  are_collinear by A1,Th3;
  hence thesis;
end;
