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Theorems · Theorem · order theory

List.sum_nonneg

∀ {M : Type u_3} [inst : AddMonoid M] [inst_1 : Preorder M] [AddLeftMono M] {l : List M}, (∀ x ∈ l, 0 ≤ x) → 0 ≤ l.sum
Defined in
Mathlib.Algebra.Order.BigOperators.Group.List
Cited by
3 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
AddMonoidPreorderAddLeftMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

List.single_le_sum · cited by 3List.single_le_sumPiTensorProduct.projectiveSeminormAux_nonneg · cited by 1PiTensorProduct.projectiv…Multiset.sum_nonneg · cited by 0Multiset.sum_nonnegPreorder · cited by 7952PreorderAddMonoid · cited by 2864AddMonoidle_refl · cited by 2061le_reflAddLeftMono · cited by 687AddLeftMonoadd_nonneg · cited by 104add_nonnegList.sum_nonnegCITED BYCITES

Cites5

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Cited by3

Results whose statement or proof uses this declaration.