Theorems · Theorem · group theory
finsum_nonneg
∀ {α : Sort u_4} {M : Type u_7} [inst : AddCommMonoid M] [inst_1 : Preorder M] [IsOrderedAddMonoid M] {f : α → M},
(∀ (i : α), 0 ≤ f i) → 0 ≤ ∑ᶠ (i : α), f i- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 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.
- AddCommMonoidstatement and proof · cited by 12,281
- Preorderstatement and proof · cited by 7,952
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- le_rflproof · cited by 1,558
- finsumstatement · cited by 286
- add_nonnegproof · cited by 104
- finsum_inductionproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- tsum_nonnegproof · cited by 18
- Function.locallyFinsuppWithin.logCounting_nonnegproof · cited by 3
- IsOpen.exists_contMDiff_support_eqproof · cited by 1
- PartitionOfUnity.sum_nonnegproof · cited by 1