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

theorem
  z1 <> z2 iff 0 < |.z1 - z2.|
proof
  thus z1 <> z2 implies 0 < |.z1 - z2.|
  proof
    assume z1 <> z2;
    then |.z1 - z2.| <> 0 by Th61;
    hence thesis;
  end;
  thus thesis;
end;
