Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.normalizedFactors_multiset_prod
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
(s : Multiset α),
0 ∉ s →
UniqueFactorizationMonoid.normalizedFactors s.prod =
(Multiset.map UniqueFactorizationMonoid.normalizedFactors s).sum- Cited by
- 0 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites21
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
- Nontrivialproof · cited by 2,416
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.mapstatement and proof · cited by 876
- Multiset.prodstatement and proof · cited by 528
- Multiset.sumstatement and proof · cited by 388
- Multiset.consproof · cited by 313
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- subsingleton_or_nontrivialproof · cited by 161
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- Multiset.map_consproof · cited by 93
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