Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.prod_normalizedFactors
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
{a : α}, a ≠ 0 → Associated (UniqueFactorizationMonoid.normalizedFactors a).prod a- Cited by
- 23 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetproof · cited by 2,627
- CommMonoidproof · cited by 2,264
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.mapproof · cited by 876
- Multiset.prodstatement and proof · cited by 528
- Associatedstatement and proof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associatesproof · cited by 210
- NormalizationMonoidstatement and proof · cited by 165
- Multiset.map_mapproof · cited by 151
- UniqueFactorizationMonoid.normalizedFactorsstatement · cited by 151
- Associates.mkproof · cited by 137
Cited by23
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.dvd_of_mem_normalizedFactorsproof · cited by 20
- UniqueFactorizationMonoid.dvd_iff_normalizedFactors_le_normalizedFactorsproof · cited by 11
- UniqueFactorizationMonoid.normalizedFactors_mulproof · cited by 11
- UniqueFactorizationMonoid.normalizedFactors_irreducibleproof · cited by 10
- UniqueFactorizationMonoid.normalizedFactors_oneproof · cited by 8
- UniqueFactorizationMonoid.exists_mem_normalizedFactors_of_dvdproof · cited by 8
- UniqueFactorizationMonoid.radical_dvd_selfproof · cited by 7
- Nat.factors_eqproof · cited by 5
- Ideal.prod_normalizedFactors_eq_selfproof · cited by 4
- UniqueFactorizationMonoid.normalizedFactors_prod_of_primeproof · cited by 2
- DivisorChain.element_of_chain_eq_pow_second_of_chainproof · cited by 1