Theorems · Theorem · number theory
Nat.factors_eq
∀ (n : ℕ), UniqueFactorizationMonoid.normalizedFactors n = ↑n.primeFactorsList
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement · cited by 2,804
- Multisetstatement · cited by 2,627
- Multiset.prodproof · cited by 528
- Associatedproof · cited by 296
- Multiset.ofListstatement and proof · cited by 290
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- Nat.primeFactorsListstatement and proof · cited by 105
- Multiset.Relproof · cited by 47
- Nat.prime_of_mem_primeFactorsListproof · cited by 30
- UniqueFactorizationMonoid.prod_normalizedFactorsproof · cited by 23
- Nat.prime_iffproof · cited by 20
- UniqueFactorizationMonoid.irreducible_of_normalized_factorproof · cited by 15
Cited by5
Results whose statement or proof uses this declaration.
- ArithmeticFunction.cardFactors_mulproof · cited by 6
- Nat.squarefree_iff_nodup_primeFactorsListproof · cited by 4
- UniqueFactorizationMonoid.primeFactors_eq_natPrimeFactorsproof · cited by 1
- ArithmeticFunction.IsMultiplicative.prodPrimeFactors_add_of_squarefreeproof · cited by 1
- Nat.moebius_eqproof · cited by 0