Theorems · Theorem · number theory
Nat.mem_primeFactorsList
∀ {n p : ℕ}, n ≠ 0 → (p ∈ n.primeFactorsList ↔ Nat.Prime p ∧ p ∣ n)- Defined in
- Mathlib.Data.Nat.Factors
- Cited by
- 9 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.
Cites5
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.dvd_of_mem_primeFactorsListproof · cited by 8
- Nat.mem_primeFactorsList_iff_dvdproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- Nat.mem_primeFactorsList_mulproof · cited by 5
- jacobiSym.eq_zero_iff_not_coprimeproof · cited by 3
- IsPrimitiveRoot.sub_one_norm_isPrimePowproof · cited by 2
- Nat.mem_factoredNumbers_of_dvdproof · cited by 1
- Nat.pow_mul_mem_factoredNumbersproof · cited by 0
- Nat.pow_mul_mem_smoothNumbersproof · cited by 0
- isPrimePow_iff_unique_prime_dvdproof · cited by 0
- Nat.prod_mem_factoredNumbersproof · cited by 0
- Nat.finMulAntidiag_existsUnique_prime_dvdproof · cited by 0