theorem Th21:
  A is_line & not a in A & not b in A & b in half-plane(A,a) implies
  a in half-plane(A,b)
  proof
    assume A is_line & not a in A & not b in A & b in half-plane(A,a);
    then ex x be POINT of S st x = b & A out x,a;
    then A out a,b;
    hence thesis;
  end;
