Theorems · Theorem · group theory
dvd_dvd_iff_associated
∀ {M : Type u_1} [inst : MonoidWithZero M] [IsLeftCancelMulZero M] {a b : M}, a ∣ b ∧ b ∣ a ↔ Associated a b- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 13 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.
- MonoidWithZerostatement and proof · cited by 456
- Associatedstatement and proof · cited by 296
- IsLeftCancelMulZerostatement and proof · cited by 48
- associated_of_dvd_dvdproof · cited by 28
- Associated.dvd_dvdproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.span_singleton_eq_span_singletonproof · cited by 15
- UniqueFactorizationMonoid.normalizedFactors_irreducibleproof · cited by 10
- normalize_eq_normalize_iffproof · cited by 3
- Int.associated_iff_natAbsproof · cited by 2
- UniqueFactorizationMonoid.prod_normalizedFactors_eqproof · cited by 1