∀ {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 a_1 : S} (e_a : a = a_1) (a_mem : a ∈ P ^ i),
  p.quotientToQuotientRangePowQuotSucc P a_mem = p.quotientToQuotientRangePowQuotSucc P ⋯