Theorems · Theorem · order theory
Fintype.sum_eq_zero_iff_of_nonpos
∀ {ι : Type u_9} {M : Type u_10} [inst : Fintype ι] [inst_1 : AddCommMonoid M] [inst_2 : PartialOrder M] [AddLeftMono M]
{f : ι → M}, f ≤ 0 → (∑ i, f i = 0 ↔ f = 0)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- AddLeftMonostatement and proof · cited by 687
- Finset.mem_univproof · cited by 361
- Finset.sum_eq_zero_iff_of_nonposproof · cited by 2
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