Theorems · Theorem · commutative algebra
Associates.FactorSet.prod_eq_zero_iff
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [IsCancelMulZero α] [Nontrivial α] (p : Associates.FactorSet α),
p.prod = 0 ↔ p = ⊤- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 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.
- Top.topstatement and proof · cited by 9,680
- Multisetstatement and proof · cited by 2,627
- Nontrivialstatement and proof · cited by 2,416
- WithTop.someproof · cited by 1,128
- CommMonoidWithZerostatement and proof · cited by 913
- Subtype.propproof · cited by 505
- Irreduciblestatement and proof · cited by 496
- Associatesstatement and proof · cited by 210
- IsCancelMulZerostatement and proof · cited by 177
- WithTop.recTopCoeproof · cited by 107
- Multiset.mem_mapproof · cited by 72
- Associates.FactorSetstatement and proof · cited by 52
Cited by2
Results whose statement or proof uses this declaration.
- Associates.FactorSet.uniqueproof · cited by 5
- Associates.factors_eq_top_iff_zeroproof · cited by 1