Theorems · Theorem · number theory
Nat.prime_dvd_prime_iff_eq
∀ {p q : ℕ}, Nat.Prime p → Nat.Prime q → (p ∣ q ↔ p = q)- Defined in
- Mathlib.Data.Nat.Prime.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext
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 and proof · cited by 2,059
- Nat.Prime.two_leproof · cited by 53
- Nat.dvd_prime_two_leproof · cited by 3
Cited by15
Results whose statement or proof uses this declaration.
- Nat.Prime.coprime_iff_not_dvdproof · cited by 38
- ZMod.unitsMap_surjectiveproof · cited by 7
- padicValNat_primesproof · cited by 2
- Nat.Prime.even_iffproof · cited by 2
- Choose.primeFactors_gcd_choose_of_isPrimePowproof · cited by 1
- X_pow_sub_C_irreducible_of_prime_powproof · cited by 1
- Char.card_pow_cardproof · cited by 1
- FiniteField.two_pow_cardproof · cited by 1
- Nat.prime_eq_prime_of_dvd_powproof · cited by 1
- IsPrimitiveRoot.prime_dvd_of_dvd_norm_sub_oneproof · cited by 1
- Nat.pepin_primalityproof · cited by 1
- ZMod.isCyclic_units_iff_of_oddproof · cited by 1