theorem Th23:
  the_midpoint_of_the_segment(A,B) = the_midpoint_of_the_segment(B,A)
  proof
    the_midpoint_of_the_segment(A,B) = 1/2*(B+A) by Th22
                              .= the_midpoint_of_the_segment(B,A) by Th22;
    hence thesis;
  end;
