Theorems · Theorem · order theory

List.prod_min_le

∀ {α : Type u_2} {M : Type u_3} [inst : Monoid M] [inst_1 : LinearOrder M] [MulLeftMono M] [MulRightMono M] (l : List α)
  (f g : α → M), (List.map (fun i => min (f i) (g i)) l).prod ≤ min (List.map f l).prod (List.map g l).prod

Defined in

Mathlib.Algebra.Order.BigOperators.Group.List

Cited by

1 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Quot.sound

Assumes

MonoidLinearOrderMulLeftMonoMulRightMono