∀ (n : ℕ) {m p k : ℕ} [hp : Fact (Nat.Prime p)] (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  (P : Ideal (NumberField.RingOfIntegers K)) [hP₁ : P.IsPrime] [hP₂ : P.LiesOver (Ideal.span {↑p})]
  [IsCyclotomicExtension {n} ℚ K], n = p ^ (k + 1) * m → ¬p ∣ m → (Ideal.span {↑p}).inertiaDeg P = orderOf ↑p