Theorems · Theorem · order theory

Finset.expect_lt_expect

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

Defined in

Mathlib.Algebra.Order.BigOperators.Expect

Cited by

4 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidPartialOrderIsOrderedCancelAddMonoidModulePosSMulStrictMono