Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.exists_mem_factors_of_dvd
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {a p : α},
a ≠ 0 → Irreducible p → p ∣ a → ∃ q ∈ UniqueFactorizationMonoid.factors a, Associated p q- Cited by
- 4 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement · cited by 2,627
- MulZeroClass.mul_zeroproof · cited by 2,091
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement and proof · cited by 496
- Multiset.consproof · cited by 313
- Associatedstatement and proof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associated.symmproof · cited by 87
- Multiset.prod_consproof · cited by 68
- UniqueFactorizationMonoid.factorsstatement and proof · cited by 55
- Multiset.Relproof · cited by 47
- Multiset.mem_consproof · cited by 29
Cited by4
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.mem_normalizedFactors_iff'proof · cited by 3
- Associates.mem_factors'_of_dvdproof · cited by 2
- UniqueFactorizationMonoid.exists_mem_factorsproof · cited by 1
- UniqueFactorizationMonoid.factors_eq_singleton_of_irreducibleproof · cited by 0