Theorems · Theorem · commutative algebra

Associates.count_factors_eq_find_of_dvd_pow

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α]
  [inst_2 : DecidableEq (Associates α)] [inst_3 : (p : Associates α) → Decidable (Irreducible p)] {a p : Associates α},
  Irreducible p → ∀ [inst_4 : (n : ℕ) → Decidable (a ∣ p ^ n)] {n : ℕ} (h : a ∣ p ^ n), Nat.find ⋯ = p.count a.factors

Defined in

Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet

Cited by

1 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroUniqueFactorizationMonoidDecidableEqDecidableDecidable