Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.mem_normalizedFactors_eq_of_associated
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
{a b c : α},
a ∈ UniqueFactorizationMonoid.normalizedFactors c →
b ∈ UniqueFactorizationMonoid.normalizedFactors c → Associated a b → a = b- Cited by
- 0 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- Associatedstatement and proof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- normalizeproof · cited by 137
- UniqueFactorizationMonoid.normalize_normalized_factorproof · cited by 9
- normalize_eq_normalize_iffproof · cited by 3
- Associated.dvd_dvdproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.