Theorems · Theorem · order theory
Finset.sum_mono_set_of_nonneg
∀ {ι : Type u_1} {N : Type u_5} [inst : AddCommMonoid N] [inst_1 : Preorder N] {f : ι → N} [AddLeftMono N],
(∀ (x : ι), 0 ≤ f x) → Monotone fun s => ∑ x ∈ s, f x- Cited by
- 5 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Preorderstatement and proof · cited by 7,952
- Finset.sumstatement · cited by 5,195
- Monotonestatement · cited by 1,397
- AddLeftMonostatement and proof · cited by 687
- Finset.sum_le_sum_of_subset_of_nonnegproof · cited by 31
Cited by5
Results whose statement or proof uses this declaration.
- summable_of_sum_leproof · cited by 4
- hasSum_of_isLUB_of_nonnegproof · cited by 2
- isLUB_hasSumproof · cited by 1
- MeasureTheory.tendsto_sum_indicator_atTop_iffproof · cited by 1
- Set.infinite_iff_tendsto_sum_indicator_atTopproof · cited by 1