Theorems · Theorem · commutative algebra

Associates.dvd_count_of_dvd_count_mul

∀ {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 b : Associates α},
  b ≠ 0 →
    ∀ {p : Associates α},
      Irreducible p →
        (∀ (d : Associates α), d ∣ a → d ∣ b → ¬Prime d) →
          ∀ {k : ℕ}, k ∣ p.count (a * b).factors → k ∣ p.count a.factors

Defined in

Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet

Cited by

1 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroUniqueFactorizationMonoidDecidableEqDecidable