theorem Th21:
  the_midpoint_of_the_segment(A,B) in LSeg(A,B)
  proof
    consider C such that
A1: C in LSeg(A,B) and
A2: C = the_midpoint_of_the_segment(A,B) and
    |.A-C.| = half_length(A,B) by Def1;
    thus thesis by A1,A2;
  end;
