Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.normalizedFactors.congr_simp
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
(a a_1 : α), a = a_1 → UniqueFactorizationMonoid.normalizedFactors a = UniqueFactorizationMonoid.normalizedFactors a_1- Cited by
- 5 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
Cited by5
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactors_powproof · cited by 8
- UniqueFactorizationMonoid.primeFactors_radicalproof · cited by 5
- Ideal.IsDedekindDomain.emultiplicity_map_eq_ramificationIdx'_mulproof · cited by 2
- emultiplicity_prime_le_emultiplicity_image_by_factor_orderIsoproof · cited by 1
- Polynomial.leadingCoeff_mul_prod_normalizedFactorsproof · cited by 0