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Unique factorization of natural numbers

Main definitions

• Nat.instUniqueFactorizationMonoid: the natural numbers have unique factorization

instance Nat.instWfDvdMonoid : WfDvdMonoid ℕ

instance Nat.instUniqueFactorizationMonoid : UniqueFactorizationMonoid ℕ

theorem Nat.factors_eq (n : ℕ) : UniqueFactorizationMonoid.normalizedFactors n = ↑n.primeFactorsList

theorem Nat.factors_multiset_prod_of_irreducible {s : Multiset ℕ} (h : ∀ x ∈ s, Irreducible x) : UniqueFactorizationMonoid.normalizedFactors s.prod = s