∀ {α : Type u_1} {p : Multiset α → Sort u_3} {n : ℕ}
  (H : (t₁ : Multiset α) → ({t₂ : Multiset α} → t₂.card ≤ n → t₁ < t₂ → p t₂) → t₁.card ≤ n → p t₁) (s : Multiset α),
  Multiset.strongDownwardInduction H s = H s fun {t} ht _h => Multiset.strongDownwardInduction H t ht