Theorems · Theorem · order theory

Finset.expect_eq_zero_iff_of_nonpos

∀ {ι : Type u_1} {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α]
  [inst_3 : Module ℚ≥0 α] {s : Finset ι} {f : ι → α},
  (∀ i ∈ s, f i ≤ 0) → ((s.expect fun i => f i) = 0 ↔ ∀ i ∈ s, f i = 0)

Defined in

Mathlib.Algebra.Order.BigOperators.Expect

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidPartialOrderIsOrderedAddMonoidModule