Theorems · Theorem · order theory

Finset.sum_pos

∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : Preorder M] [IsOrderedCancelAddMonoid M] {f : ι → M}
  {s : Finset ι} [AddLeftStrictMono M], (∀ i ∈ s, 0 < f i) → s.Nonempty → 0 < ∑ i ∈ s, f i

Defined in

Mathlib.Algebra.Order.BigOperators.Group.Finset

Cited by

15 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidPreorderIsOrderedCancelAddMonoidAddLeftStrictMono