Theorems · Theorem · number theory
Nat.prime_of_mem_primeFactors
∀ {n p : ℕ}, p ∈ n.primeFactors → Nat.Prime p- Defined in
- Mathlib.Data.Nat.PrimeFin
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 2,059
- Nat.primeFactorsstatement and proof · cited by 129
- Nat.mem_primeFactorsproof · cited by 12
Cited by30
Results whose statement or proof uses this declaration.
- Nat.factorization_prod_pow_eq_self_of_le_factorizationproof · cited by 5
- BoundingSieve.nu_pos_of_dvd_prodPrimesproof · cited by 4
- Nat.dvd_prod_primeFactors_pow_selfproof · cited by 4
- ArithmeticFunction.IsMultiplicative.map_prod_of_subset_primeFactorsproof · cited by 3
- Nat.factorizationEquivproof · cited by 3
- Nat.pos_of_mem_primeFactorsproof · cited by 3
- DirichletCharacter.LFunctionTrivChar_residue_oneproof · cited by 2
- Nat.primeFactors_lcmUptoproof · cited by 2
- Group.isNilpotent_of_product_of_sylow_groupproof · cited by 2
- Nat.totient_eq_prod_factorizationproof · cited by 2
- ZMod.isSquare_neg_one_iff_forall_mem_primeFactors_mod_four_ne_threeproof · cited by 2
- DirichletCharacter.LFunctionTrivChar₁_apply_one_ne_zeroproof · cited by 1