{R : Type u_4} →
  {S : Type u_5} →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          (f : Polynomial R) →
            (monic_f : f.Monic) →
              (g : Polynomial R) →
                (cond : ∃ p₁ p₂ n, Polynomial.derivative f * p₁ + f * p₂ = g ^ n) →
                  (x : S) →
                    (hasMap : { f := f, monic_f := monic_f, g := g, cond := cond }.HasMap x) →
                      Function.Bijective ⇑({ f := f, monic_f := monic_f, g := g, cond := cond }.lift x hasMap) →
                        StandardEtalePresentation R S