Theorems · Theorem · number theory
Nat.prime_iff
∀ {p : ℕ}, Nat.Prime p ↔ Prime p- Defined in
- Mathlib.Data.Nat.Prime.Defs
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Primestatement · cited by 277
- Nat.Prime.ne_zeroproof · cited by 109
- Prime.irreducibleproof · cited by 54
- Irreducible.not_isUnitproof · cited by 42
- Nat.Prime.dvd_mulproof · cited by 12
Cited by20
Results whose statement or proof uses this declaration.
- Nat.prime_iff_prime_intproof · cited by 27
- Nat.Prime.primeproof · cited by 19
- Nat.dvd_prime_powproof · cited by 13
- Nat.factors_eqproof · cited by 5
- Nat.Prime.isPrimePowproof · cited by 5
- Prime.nat_primeproof · cited by 4
- Nat.mem_primeFactorsList_iff_dvdproof · cited by 4
- IsCyclotomicExtension.discr_prime_powproof · cited by 3
- Nat.irreducible_iff_primeproof · cited by 3
- IsPrimePow.minFac_pow_factorization_eqproof · cited by 2
- Nat.Primes.prodNatEquiv_applystatement · cited by 2
- IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_twoproof · cited by 2