Theorems · Theorem · number theory
Nat.mem_primeFactorsList_mul
∀ {a b : ℕ}, a ≠ 0 → b ≠ 0 → ∀ {p : ℕ}, p ∈ (a * b).primeFactorsList ↔ p ∈ a.primeFactorsList ∨ p ∈ b.primeFactorsList- Defined in
- Mathlib.Data.Nat.Factors
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 80 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.Primeproof · cited by 2,059
- mul_ne_zeroproof · cited by 178
- Nat.primeFactorsListstatement and proof · cited by 105
- Nat.Prime.dvd_mulproof · cited by 12
- Nat.mem_primeFactorsListproof · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- Nat.primeFactors_mulproof · cited by 6
- Nat.mem_primeFactorsList_mul_leftproof · cited by 1
- Nat.mem_primeFactorsList_mul_of_coprimeproof · cited by 1
- Nat.pow_mul_mem_factoredNumbersproof · cited by 0
- Nat.pow_mul_mem_smoothNumbersproof · cited by 0