Theorems · Theorem · commutative algebra
Associates.factors_le
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {a b : Associates α},
a.factors ≤ b.factors ↔ a ≤ b- Cited by
- 2 results in Mathlib
- Foundations
- Depth 57 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 · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement · cited by 496
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associatesstatement and proof · cited by 210
- Associates.factorsstatement and proof · cited by 97
- Associates.FactorSetstatement · cited by 52
- Associates.FactorSet.prodproof · cited by 20
- Associates.factors_prodproof · cited by 9
- Associates.factors_monoproof · cited by 3
- Associates.prod_monoproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.mem_integers_of_valuation_le_oneproof · cited by 1
- Associates.prime_pow_le_iff_le_bcountproof · cited by 1