reserve a,b,c,d,e,f for Real,
        g           for positive Real,
        x,y         for Complex,
        S,T         for Element of REAL 2,
        u,v,w       for Element of TOP-REAL 3;

theorem
  a^2 * (1/(b^2)) = (a/b)^2
  proof
    a^2 * (1/(b^2)) = a * a * ((1/b) * (1/b)) by XCMPLX_1:102
    .= a * (a * (1/b)) * (1/b)
    .= a * ((a * 1)/b) * (1/b) by XCMPLX_1:74
    .= (a/b) * (a *(1/b))
    .= (a/b) * ((a * 1)/b) by XCMPLX_1:74
    .= (a / b)^2;
    hence thesis;
  end;
