Theorems · Theorem · ring theory
Finsupp.prod_eq_zero_iff
∀ {α : Type u_1} {ι : Type u_2} {β : Type u_7} [inst : Zero α] [inst_1 : CommMonoidWithZero β] [Nontrivial β]
[NoZeroDivisors β] {f : ι →₀ α} {g : ι → α → β}, f.prod g = 0 ↔ ∃ i ∈ f.support, g i (f i) = 0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsetstatement · cited by 13,712
- Finsuppstatement and proof · cited by 5,255
- Nontrivialstatement and proof · cited by 2,416
- CommMonoidWithZerostatement and proof · cited by 913
- Finsupp.supportstatement · cited by 828
- NoZeroDivisorsstatement and proof · cited by 545
- Finsupp.prodstatement · cited by 231
- Finset.prod_eq_zero_iffproof · cited by 9
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