Theorems · Theorem · number theory
Nat.coprime_primeFactorsList_disjoint
∀ {a b : ℕ}, a.Coprime b → a.primeFactorsList.Disjoint b.primeFactorsListThe sets of factors of coprime a and b are disjoint
- Defined in
- Mathlib.Data.Nat.Factors
- Cited by
- 3 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.Primeproof · cited by 2,059
- Nat.primeFactorsListstatement and proof · cited by 105
- Nat.prime_of_mem_primeFactorsListproof · cited by 30
- Nat.not_prime_oneproof · cited by 10
- Nat.dvd_of_mem_primeFactorsListproof · cited by 8
- Nat.eq_one_of_dvd_coprimesproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Nat.Coprime.disjoint_primeFactorsproof · cited by 4
- Nat.factorization_eq_of_coprime_leftproof · cited by 1
- ArithmeticFunction.cardDistinctFactors_mulproof · cited by 1