Theorems · Theorem · commutative algebra
WfDvdMonoid.exists_factors
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [WfDvdMonoid α] (a : α),
a ≠ 0 → ∃ f, (∀ b ∈ f, Irreducible b) ∧ Associated f.prod a- Cited by
- 5 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_mulproof · cited by 2,841
- Multisetstatement and proof · cited by 2,627
- Units.valproof · cited by 1,966
- IsUnitproof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.prodstatement and proof · cited by 528
- Irreduciblestatement and proof · cited by 496
- Multiset.consproof · cited by 313
- Associatedstatement and proof · cited by 296
- IsUnit.unitproof · cited by 252
- Multiset.prod_consproof · cited by 68
- WfDvdMonoidstatement and proof · cited by 37
Cited by5
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.exists_prime_factorsproof · cited by 6
- IsDiscreteValuationRing.associated_pow_irreducibleproof · cited by 4
- WfDvdMonoid.not_isUnit_iff_exists_factors_eqproof · cited by 2
- PrincipalIdealRing.factors_specproof · cited by 2