Theorems · Theorem · order theory
Finset.sum_pos_iff_of_nonneg
∀ {ι : Type u_1} {N : Type u_5} [inst : AddCommMonoid N] [inst_1 : PartialOrder N] {f : ι → N} {s : Finset ι}
[AddLeftMono N], (∀ x ∈ s, 0 ≤ f x) → (0 < ∑ x ∈ s, f x ↔ ∃ x ∈ s, 0 < f x)- Cited by
- 3 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.
Cites8
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 and proof · cited by 5,195
- AddLeftMonostatement and proof · cited by 687
- Finset.sum_nonnegproof · cited by 91
- Finset.sum_eq_zero_iff_of_nonnegproof · cited by 19
- LE.le.lt_iff_ne'proof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.pow_apply_pos_iff_nonempty_pathproof · cited by 1
- Finset.sum_pos_iffproof · cited by 0
- Finset.sum_neg_iff_of_nonposproof · cited by 0