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

theorem
  z1 <> 0.F_Complex & z2 <> 0.F_Complex implies z1"* (z / z2) = z / (z1 * z2)
proof
  reconsider z19=z1,z29=z2,z9=z as Element of COMPLEX by Def1;
  assume
A1: z1 <> 0.F_Complex;
  assume
A2: z2 <> 0.F_Complex;
  then
A3: z1 * z2 <> 0.F_Complex by A1,VECTSP_1:12;
A4: z9 / z29 = z / z2 by A2,Th6;
  z1" = z19" by A1,Th5;
  hence z1"* (z / z2) = z9 / (z19 * z29) by A4,XCMPLX_1:220
    .= z / (z1 * z2) by A3,Th6;
end;
