Theorems · Theorem · number theory
Nat.dvd_of_forall_prime_mul_dvd
∀ {a b : ℕ}, (∀ (p : ℕ), Nat.Prime p → p ∣ a → p * a ∣ b) → a ∣ b- Defined in
- Mathlib.Data.Nat.Prime.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- eq_or_neproof · cited by 1,117
- transproof · cited by 111
- dvd_mul_leftproof · cited by 47
- one_dvdproof · cited by 37
- Nat.exists_prime_and_dvdproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Commute.orderOf_mul_eq_right_of_forall_prime_mul_dvdproof · cited by 2
- AddCommute.addOrderOf_add_eq_right_of_forall_prime_mul_dvdproof · cited by 2