Theorems · Theorem · commutative algebra
Associates.sup_mul_inf
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] (a b : Associates α),
(a ⊔ b) * (a ⊓ b) = a * b- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Nontrivialproof · cited by 2,416
- MulZeroClass.mul_zeroproof · cited by 2,091
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- sup_of_le_leftproof · cited by 218
- Associatesstatement and proof · cited by 210
- inf_of_le_leftproof · cited by 186
- Associates.factorsproof · cited by 97
- Associates.FactorSetproof · cited by 52
- Associates.FactorSet.prodproof · cited by 20
- Associates.factors_mulproof · cited by 4
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