theorem Th38:
  A is_line & A9 is_line & A <> A9 implies ex r being POINT of S st
  not r in A & r in A9
  proof
    assume that
A1: A is_line and
A2: A9 is_line and
A3: A <> A9;
    consider p9,q9 be POINT of S such that
A4: p9 <> q9 and
A5: A9 = Line(p9,q9) by A2;
    not (p9 in A & q9 in A) by A1,A3,A4,A5,GTARSKI3:87;
    hence thesis by A5,GTARSKI3:83;
  end;
