Theorems · Theorem · number theory
Nat.Prime.dvd_mul
∀ {p m n : ℕ}, Nat.Prime p → (p ∣ m * n ↔ p ∣ m ∨ p ∣ n)- Defined in
- Mathlib.Data.Nat.Prime.Defs
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.coprime_iff_not_dvdproof · cited by 38
- Dvd.dvd.mul_rightproof · cited by 15
- Dvd.dvd.mul_leftproof · cited by 14
Cited by12
Results whose statement or proof uses this declaration.
- Nat.prime_iff_prime_intproof · cited by 27
- Nat.prime_iffproof · cited by 20
- ZMod.unitsMap_surjectiveproof · cited by 7
- Nat.mem_primeFactorsList_mulproof · cited by 5
- Nat.Prime.dvd_choose_addproof · cited by 2
- Nat.Prime.not_dvd_mulproof · cited by 2
- Int.Prime.dvd_mulproof · cited by 2
- Nat.Prime.dvd_or_dvdproof · cited by 1
- Nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mulproof · cited by 1
- Nat.Prime.mul_eq_prime_sq_iffproof · cited by 1
- prime_two_or_dvd_of_dvd_two_mul_pow_self_twoproof · cited by 0
- Nat.coprime_mul_succproof · cited by 0