reserve a, b, c, d, e for Complex;

theorem
  for a,b st b<>0 ex e st a=b/e
proof
  let a,b;
  assume
A1: b<>0;
  per cases;
  suppose
A2: a = 0;
    take 0;
    b/0 = b*0" by XCMPLX_0:def 9;
    hence thesis by A2;
  end;
  suppose
A3: a <> 0;
    take e=b/a;
    thus a=a*1 .=a*(e*e") by A1,A3,XCMPLX_0:def 7
      .=a*e*e"
      .=a*(a"*b)*e" by XCMPLX_0:def 9
      .=a*a"*b*e"
      .=1*b*e" by A3,XCMPLX_0:def 7
      .=b/e by XCMPLX_0:def 9;
  end;
end;
