theorem Th48:
  A is_line & not a in A implies a in Plane(A,a)
  proof
    assume that
A1: A is_line and
A2: not a in A;
    A out a,a & Plane(A,a)
        = {x where x is POINT of S : A out x,a
                                      or x in A
                                      or between a,A,x}
          by A1,A2,Th32,Th17;
    hence a in Plane(A,a);
  end;
