Theorems · Theorem · commutative algebra

Associates.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 : Associates α},
  a ≠ 0 →
    ∀ {b : Associates α},
      b ≠ 0 → ∀ {p : Associates α}, Irreducible p → p.count (a * b).factors = p.count a.factors + p.count b.factors

Defined in

Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet

Cited by

7 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroUniqueFactorizationMonoidDecidableEqDecidable