theorem Th44:
  u+ID(M) = u
proof
  set a = the Element of M;
  consider b such that
A1: u = vect(a,b) by Th35;
  u+ID(M) = vect(a,b)+vect(b,b) by A1,Th32
    .= u by A1,Th40;
  hence thesis;
end;
