Theorems · Theorem · order theory
Finsupp.sum_pos
∀ {ι : Type u_1} {α : Type u_3} {β : Type u_4} [inst : Zero α] [inst_1 : AddCommMonoid β] [inst_2 : Preorder β]
[IsOrderedCancelAddMonoid β] [AddLeftStrictMono β] {f : ι →₀ α} {g : ι → α → β},
(∀ i ∈ f.support, 0 < g i (f i)) → f ≠ 0 → 0 < f.sum g- Defined in
- Mathlib.Data.Finsupp.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Preorderstatement and proof · cited by 7,952
- Finsuppstatement and proof · cited by 5,255
- Finsupp.supportstatement and proof · cited by 828
- Finsupp.sumstatement · cited by 481
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- AddLeftStrictMonostatement and proof · cited by 203
- Finset.sum_posproof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- Convexity.StdSimplex.support_weights_restrictproof · cited by 2