Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors
∀ {R : Type u_2} [inst : CommMonoidWithZero R] [inst_1 : UniqueFactorizationMonoid R] [inst_2 : NormalizationMonoid R]
{a b : R} {n : ℕ},
Irreducible a →
b ≠ 0 →
(↑n ≤ emultiplicity a b ↔ Multiset.replicate n (normalize a) ≤ UniqueFactorizationMonoid.normalizedFactors b)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
- Multisetstatement and proof · cited by 2,627
- mul_assocproof · cited by 1,667
- pow_zeroproof · cited by 1,094
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.prodproof · cited by 528
- Irreduciblestatement and proof · cited by 496
- Multiset.consproof · cited by 313
- UniqueFactorizationMonoidstatement and proof · cited by 279
- pow_succ'proof · cited by 228
- NormalizationMonoidstatement and proof · cited by 165
- emultiplicitystatement · cited by 156
Cited by1
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.emultiplicity_eq_count_normalizedFactorsproof · cited by 14