Theorems · Theorem · order theory

Finset.exists_le_of_expect_le_expect

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

Defined in

Mathlib.Algebra.Order.BigOperators.Expect

Cited by

2 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidLinearOrderIsOrderedCancelAddMonoidModulePosSMulStrictMono