Theorems · Theorem · number theory
Nat.prime_iff_prime_int
∀ {p : ℕ}, Nat.Prime p ↔ Prime ↑p- Defined in
- Mathlib.Data.Nat.Prime.Int
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.cast_oneproof · cited by 2,501
- Nat.Primestatement and proof · cited by 2,059
- Primestatement and proof · cited by 277
- Nat.Prime.posproof · cited by 83
- Nat.Prime.ne_oneproof · cited by 61
- Nat.prime_iffproof · cited by 20
- Nat.Prime.dvd_mulproof · cited by 12
- Nat.isUnit_iffproof · cited by 7
- Int.isUnit_iff_natAbs_eqproof · cited by 6
Cited by27
Results whose statement or proof uses this declaration.
- Int.prime_iff_natAbs_primeproof · cited by 11
- padicValRat.mulproof · cited by 5
- Int.ModEq.pow_card_sub_one_eq_oneproof · cited by 3
- padicValRat.defnproof · cited by 2
- ZMod.eq_zero_iff_gcd_ne_oneproof · cited by 2
- Int.emultiplicity_pow_sub_powproof · cited by 2
- Ideal.exists_isMaximal_dvd_of_dvd_absNormproof · cited by 2
- Int.prime_ofNat_iffproof · cited by 2
- Int.exists_prime_and_dvdproof · cited by 1
- IsCyclotomicExtension.Rat.zeta_sub_one_dvd_intCast_iffproof · cited by 1
- cyclotomic_comp_X_add_one_isEisensteinAtproof · cited by 1