Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.normalizedFactors_mul
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
{x y : α},
x ≠ 0 →
y ≠ 0 →
UniqueFactorizationMonoid.normalizedFactors (x * y) =
UniqueFactorizationMonoid.normalizedFactors x + UniqueFactorizationMonoid.normalizedFactors y- Cited by
- 11 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.
Cites27
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
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.mapproof · cited by 876
- Multiset.prodproof · cited by 528
- Associatedproof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Multiset.map_congrproof · cited by 232
- mul_ne_zeroproof · cited by 178
- NormalizationMonoidstatement and proof · cited by 165
- Multiset.map_mapproof · cited by 151
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- normalizeproof · cited by 137
Cited by11
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.dvd_iff_normalizedFactors_le_normalizedFactorsproof · cited by 11
- UniqueFactorizationMonoid.normalizedFactors_powproof · cited by 8
- ArithmeticFunction.cardFactors_mulproof · cited by 6
- Ideal.ramificationIdx'_algebra_towerproof · cited by 2
- UniqueFactorizationMonoid.primeFactors_mul_eq_unionproof · cited by 2
- Nat.divisors_filter_squarefreeproof · cited by 1
- UniqueFactorizationMonoid.normalizedFactors_prod_eqproof · cited by 0
- factorization_mulproof · cited by 0
- UniqueFactorizationMonoid.normalizedFactors_multiset_prodproof · cited by 0