reserve z,z1,z2,z3,z4 for Element of F_Complex;

theorem
  |.z1.| - |.z2.| <= |.z1 - z2.|
proof
  reconsider z19=z1,z29=z2 as Element of COMPLEX by Def1;
  z19 - z29 = z1 - z2 by Th3;
  hence thesis by COMPLEX1:59;
end;
