Theorems · Theorem · number theory
Nat.mem_primeFactorsList_iff_dvd
∀ {n p : ℕ}, n ≠ 0 → Nat.Prime p → (p ∈ n.primeFactorsList ↔ p ∣ n)- Defined in
- Mathlib.Data.Nat.Factors
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 77 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.
- Nat.Primestatement and proof · cited by 2,059
- Nat.primeFactorsListstatement and proof · cited by 105
- Nat.prime_of_mem_primeFactorsListproof · cited by 30
- Nat.prime_iffproof · cited by 20
- Nat.prod_primeFactorsListproof · cited by 15
- List.dvd_prodproof · cited by 3
- mem_list_primes_of_dvd_prodproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Nat.mem_primeFactorsListproof · cited by 9
- Nat.dvd_of_mem_primeFactorsListproof · cited by 8
- Nat.Prime.factorization_pos_of_dvdproof · cited by 3
- Nat.Prime.factoredNumbers_coprimeproof · cited by 2