Theorems · Theorem · order theory
Finset.sum_eq_zero_iff_of_nonpos
∀ {ι : Type u_1} {N : Type u_5} [inst : AddCommMonoid N] [inst_1 : PartialOrder N] {f : ι → N} {s : Finset ι}
[AddLeftMono N], (∀ i ∈ s, f i ≤ 0) → (∑ i ∈ s, f i = 0 ↔ ∀ i ∈ s, f i = 0)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Finset.sumstatement · cited by 5,195
- AddLeftMonostatement and proof · cited by 687
- Finset.sum_eq_zero_iff_of_nonnegproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- Finset.expect_eq_zero_iff_of_nonposproof · cited by 1
- Fintype.sum_eq_zero_iff_of_nonposproof · cited by 0