Theorems · Theorem · commutative algebra
prime_factors_unique
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [IsCancelMulZero α] {f g : Multiset α},
(∀ x ∈ f, Prime x) → (∀ x ∈ g, Prime x) → Associated f.prod g.prod → Multiset.Rel Associated f g- Cited by
- 3 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement and proof · cited by 2,627
- IsUnitproof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.prodstatement and proof · cited by 528
- Multiset.consproof · cited by 313
- Associatedstatement and proof · cited by 296
- Primestatement and proof · cited by 277
- IsCancelMulZerostatement and proof · cited by 177
- Dvd.dvd.transproof · cited by 148
- Classical.decEqproof · cited by 134
- Multiset.induction_onproof · cited by 109
- Multiset.eraseproof · cited by 93
Cited by3
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.factors_uniqueproof · cited by 14
- UniqueFactorizationMonoid.normalizedFactors_prod_of_primeproof · cited by 2
- WfDvdMonoid.of_exists_prime_factorsproof · cited by 1