Theorems · Theorem · commutative algebra
support_factorization
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] [inst_2 : NormalizationMonoid α]
[inst_3 : DecidableEq α] {n : α}, (factorization n).support = (UniqueFactorizationMonoid.normalizedFactors n).toFinsetThe support of factorization n is exactly the Finset of normalized factors
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- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- CommMonoidWithZerostatement and proof · cited by 913
- Finsupp.supportstatement · cited by 828
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Multiset.toFinsetstatement and proof · cited by 230
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- factorizationstatement · cited by 9
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