Theorems · Theorem · number theory
Nat.perm_primeFactorsList_mul_of_coprime
∀ {a b : ℕ}, a.Coprime b → (a * b).primeFactorsList.Perm (a.primeFactorsList ++ b.primeFactorsList)For coprime a and b, the prime factors of a * b are the union of those of a and b
- Defined in
- Mathlib.Data.Nat.Factors
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- MulZeroClass.mul_zeroproof · cited by 2,091
- LT.lt.ne'proof · cited by 1,417
- Nat.primeFactorsListstatement and proof · cited by 105
- Nat.primeFactorsList_zeroproof · cited by 13
- Nat.primeFactorsList_oneproof · cited by 11
- Nat.perm_primeFactorsList_mulproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Nat.factorization_mul_apply_of_coprimeproof · cited by 3
- ArithmeticFunction.cardDistinctFactors_mulproof · cited by 1