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

theorem
  z2 <> 0.F_Complex implies -(z1 / z2) = (-z1) / z2 & -(z1 / z2) = z1 / (-z2)
proof
  assume
A1: z2 <> 0.F_Complex;
  then
A2: -z2 <> 0.F_Complex by VECTSP_1:28;
  reconsider z19=z1,z29=z2 as Element of COMPLEX by Def1;
A3: -z1 = -z19 by Th2;
  z1 / z2 = z19 / z29 by A1,Th6;
  hence -(z1 / z2) = -(z19 / z29) by Th2
    .= (-z19) / z29 by XCMPLX_1:187
    .= (-z1) / z2 by A3,A1,Th6;
A4: -z2 = -z29 by Th2;
  z1 / z2 = z19 / z29 by A1,Th6;
  hence -(z1 / z2) = -(z19 / z29) by Th2
    .= z19 / -(z29) by XCMPLX_1:188
    .= z1 / -z2 by A4,A2,Th6;
end;
