Theorems · Theorem · group theory

Set.multiset_sum_mem_multiset_sum

∀ {ι : Type u_1} {α : Type u_2} [inst : AddCommMonoid α] (t : Multiset ι) (f : ι → Set α) (g : ι → α),
  (∀ i ∈ t, g i ∈ f i) → (Multiset.map g t).sum ∈ (Multiset.map f t).sum

An n-ary version of Set.add_mem_add.

Defined in

Mathlib.Algebra.Group.Pointwise.Set.BigOperators

Cited by

1 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoid