Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.normalize_normalized_factor
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
{a : α}, ∀ x ∈ UniqueFactorizationMonoid.normalizedFactors a, normalize x = x- Cited by
- 9 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Multiset.map_congrproof · cited by 232
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.normalizedFactorsstatement · cited by 151
- normalizestatement and proof · cited by 137
- Multiset.mem_mapproof · cited by 72
- UniqueFactorizationMonoid.exists_prime_factorsproof · cited by 6
- normalize_idemproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactors_mulproof · cited by 11
- UniqueFactorizationMonoid.normalizedFactors_irreducibleproof · cited by 10
- UniqueFactorizationMonoid.mem_normalizedFactors_iff'proof · cited by 3
- UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactorsproof · cited by 3
- UniqueFactorizationMonoid.dvd_iff_emultiplicity_leproof · cited by 1
- UniqueFactorizationMonoid.multiplicative_of_coprimeproof · cited by 1
- UniqueFactorizationMonoid.normalizedFactors_eq_of_dvdproof · cited by 1
- UniqueFactorizationMonoid.mem_normalizedFactors_eq_of_associatedproof · cited by 0