theorem Th36:
  A is_line & a in A & p in A implies reflection(p,a) in A
  proof
    assume that
A1: A is_line and
A2: a in A and
A3: p in A;
    per cases;
    suppose p = a;
      hence thesis by A2,GTARSKI3:104;
    end;
    suppose
A4:   p <> a;
      Middle a,p,reflection(p,a) by GTARSKI3:def 13;
      then Collinear p,a,reflection(p,a) by GTARSKI4:7;
      then reflection(p,a) in Line(p,a);
      hence thesis by A4,A1,A2,A3,GTARSKI3:87;
    end;
  end;
