Theorems · Theorem · commutative algebra

Associates.prime_pow_le_iff_le_bcount

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α]
  [inst_2 : DecidableEq (Associates α)] {m p : Associates α},
  m ≠ 0 → ∀ (h₂ : Irreducible p) {k : ℕ}, p ^ k ≤ m ↔ k ≤ Associates.bcount ⟨p, h₂⟩ m.factors

Defined in

Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet

Cited by

1 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroUniqueFactorizationMonoidDecidableEq