Theorems · Theorem · order theory

Multiset.sum_map_le_sum_map

∀ {ι : Type u_1} {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : Preorder α] [AddLeftMono α] {s : Multiset ι}
  (f g : ι → α), (∀ i ∈ s, f i ≤ g i) → (Multiset.map f s).sum ≤ (Multiset.map g s).sum

Defined in

Mathlib.Algebra.Order.BigOperators.Group.Multiset

Cited by

1 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidPreorderAddLeftMono