Theorems · Theorem · number theory
Nat.Prime.prime
∀ {p : ℕ}, Nat.Prime p → Prime pAlias of the forward direction of Nat.prime_iff.
- Defined in
- Mathlib.Data.Nat.Prime.Defs
- Cited by
- 19 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.Primestatement · cited by 2,059
- Primestatement · cited by 277
- Nat.prime_iffproof · cited by 20
Cited by19
Results whose statement or proof uses this declaration.
- Nat.Prime.dvd_of_dvd_powproof · cited by 15
- ZMod.unitsMap_surjectiveproof · cited by 7
- ArithmeticFunction.vonMangoldt_apply_primeproof · cited by 4
- Nat.Prime.emultiplicity_mulproof · cited by 4
- Nat.primeFactors_prodproof · cited by 3
- Nat.Prime.dvd_primorial_iffproof · cited by 2
- Nat.Prime.emultiplicity_oneproof · cited by 2
- IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_ne_twoproof · cited by 1
- isPrimePow_of_minFac_pow_factorization_eqproof · cited by 1
- charP_zero_or_prime_powerproof · cited by 1
- Nat.Prime.emultiplicity_factorial_mul_succproof · cited by 1
- Nat.Prime.emultiplicity_pow_selfproof · cited by 1