reserve z1,z2,z3,z4,z for Quaternion;

theorem
  |.z1.|-|.z2.|<>0 implies |.z1.|^2+|.z2.|^2 -2*|.z1.|*|.z2.| >0
proof
  assume |.z1.|-|.z2.|<>0;
  then (|.z1.|-|.z2.|)^2 >0 by SQUARE_1:12;
  hence thesis;
end;
