{R : Type u} →
  [inst : CommRing R] →
    {S : Type v} →
      [inst_1 : CommRing S] →
        (p : Ideal R) →
          (P : Ideal S) →
            [inst_2 : Algebra R S] →
              [hfp : NeZero (Ideal.ramificationIdx (algebraMap R S) p P)] →
                {i : ℕ} →
                  {a : S} →
                    a ∈ P ^ i →
                      S ⧸ P →ₗ[R ⧸ p]
                        ↥(Ideal.map (Ideal.Quotient.mk (P ^ Ideal.ramificationIdx (algebraMap R S) p P)) (P ^ i)) ⧸
                          (p.powQuotSuccInclusion P i).range