reserve a,b,c,d for Real;
reserve z,z1,z2 for Complex;

theorem
  |.|.z1.| - |.z2.|.| <= |.z1 - z2.|
proof
  |.z2.| - |.z1.| <= |.z2 - z1.| by Th59;
  then -(|.z1.| - |.z2.|) <= |.z1 - z2.| by Th60;
  then
A1: -|.z1 - z2.| <= --(|.z1.| - |.z2.|) by XREAL_1:24;
  |.z1.| - |.z2.| <= |.z1 - z2.| by Th59;
  hence thesis by A1,Lm30;
end;
