Theorems · Theorem · number theory
Int.prime_iff_natAbs_prime
∀ {k : ℤ}, Prime k ↔ Nat.Prime k.natAbs- Defined in
- Mathlib.RingTheory.Int.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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_iff_prime_intproof · cited by 27
- Int.associated_natAbsproof · cited by 4
- Associated.prime_iffproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- Ideal.norm_dvd_iffproof · cited by 3
- AddCommGroup.equiv_free_prod_directSum_zmodproof · cited by 2
- IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_pow_ne_twoproof · cited by 1
- Rat.HeightOneSpectrum.prime_natGeneratorproof · cited by 1
- IsPrimitiveRoot.zeta_sub_one_prime_of_ne_twoproof · cited by 1
- NumberField.exists_not_isUnramifiedInproof · cited by 1
- IsPrimitiveRoot.zeta_sub_one_prime_of_two_powproof · cited by 1
- NumberField.exists_not_isUnramifiedAt_int_of_isGaloisproof · cited by 0
- Ideal.isPrime_int_iffproof · cited by 0
- Ideal.exists_isMaximal_dvd_of_dvd_absNorm'proof · cited by 0