Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.factors_rel_of_associated
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {a b : α},
Associated a b → Multiset.Rel Associated (UniqueFactorizationMonoid.factors a) (UniqueFactorizationMonoid.factors b)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Associatedstatement and proof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associated.symmproof · cited by 87
- UniqueFactorizationMonoid.factorsstatement · cited by 55
- Multiset.Relstatement and proof · cited by 47
- Associated.transproof · cited by 22
- UniqueFactorizationMonoid.factors_prodproof · cited by 18
- UniqueFactorizationMonoid.factors_uniqueproof · cited by 14
- UniqueFactorizationMonoid.irreducible_of_factorproof · cited by 13
- UniqueFactorizationMonoid.factors_zeroproof · cited by 4
- iff_iff_and_or_not_and_notproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Associated.normalizedFactors_eqproof · cited by 2
- UniqueFactorizationMonoid.factors_of_isUnitproof · cited by 1