Theorems · Theorem · commutative algebra
Associates.prod_le
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [UniqueFactorizationMonoid α] [Nontrivial α]
{a b : Associates.FactorSet α}, a.prod ≤ b.prod ↔ a ≤ b- Cited by
- 0 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement · cited by 2,627
- Nontrivialstatement and proof · cited by 2,416
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement · cited by 496
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associatesstatement · cited by 210
- Associates.factorsproof · cited by 97
- Associates.FactorSetstatement and proof · cited by 52
- Associates.FactorSet.prodstatement and proof · cited by 20
- Associates.factors_monoproof · cited by 3
- Associates.prod_factorsproof · cited by 3
- Associates.prod_monoproof · cited by 2
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