{R : Type u} →
  [inst : CommRing R] →
    {S : Type v} →
      [inst_1 : CommRing S] →
        (p : Ideal R) →
          (P : Ideal S) →
            [inst_2 : Algebra R S] →
              (i : ℕ) →
                ↥(Ideal.map (Ideal.Quotient.mk (P ^ Ideal.ramificationIdx (algebraMap R S) p P))
                      (P ^ (i + 1))) →ₗ[R ⧸ p]
                  ↥(Ideal.map (Ideal.Quotient.mk (P ^ Ideal.ramificationIdx (algebraMap R S) p P)) (P ^ i))