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

theorem
  z1 <> 0.F_Complex & z2 <> 0.F_Complex implies (z1" / z2") = z2 / z1
proof
  reconsider z19=z1,z29=z2 as Element of COMPLEX by Def1;
  assume
A1: z1 <> 0.F_Complex;
  assume z2 <> 0.F_Complex;
  then
A2: z2" = z29" & z2" <> 0.F_Complex by Th5,VECTSP_1:25;
  z1" = z19" by A1,Th5;
  hence (z1" / z2") = (z19" / z29") by A2,Th6
    .= z29 / z19 by XCMPLX_1:214
    .= z2 / z1 by A1,Th6;
end;
