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

theorem
  z <> 0.F_Complex & z2 <> 0.F_Complex implies (z1 / z2) = (z1 * z) / (
  z2 * z) & (z1 / z2) = (z * z1) / (z * z2)
proof
  reconsider z19=z1,z29=z2,z9=z as Element of COMPLEX by Def1;
  assume
A1: z <> 0.F_Complex;
  assume
A2: z2 <> 0.F_Complex;
  then
A3: z2 * z <> 0.F_Complex by A1,VECTSP_1:12;
  thus (z1 / z2) = (z19 / z29) by A2,Th6
    .= (z19 * z9) / (z29 * z9) by A1,Th7,XCMPLX_1:91
    .= (z1 * z) / (z2 * z) by A3,Th6;
  hence thesis;
end;
