Theorems · Theorem · number theory
Nat.mem_primeFactors
∀ {n p : ℕ}, p ∈ n.primeFactors ↔ Nat.Prime p ∧ p ∣ n ∧ n ≠ 0- Defined in
- Mathlib.Data.Nat.PrimeFin
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Nat.Primestatement and proof · cited by 2,059
- Nat.primeFactorsstatement · cited by 129
Cited by12
Results whose statement or proof uses this declaration.
- Nat.prime_of_mem_primeFactorsproof · cited by 29
- Nat.dvd_of_mem_primeFactorsproof · cited by 10
- ZMod.unitsMap_surjectiveproof · cited by 7
- Nat.Prime.mem_primeFactorsproof · cited by 4
- Nat.one_lt_radical_iffproof · cited by 3
- Nat.primeFactors_prod_primeFactorsproof · cited by 2
- Nat.le_of_mem_primeFactorsproof · cited by 2
- ZMod.isSquare_neg_one_iff_forall_mem_primeFactors_mod_four_ne_threeproof · cited by 2
- isPGroup_iff_card_dvd_powproof · cited by 2
- Nat.eq_prod_primes_mul_sq_of_mem_smoothNumbersproof · cited by 1
- Nat.primeFactors_eq_emptyproof · cited by 1
- ZMod.isSquare_neg_one_iff'proof · cited by 0