Theorems · Theorem · group theory

Set.finsetSum_mem_finsetSum

∀ {ι : Type u_1} {α : Type u_2} [inst : AddCommMonoid α] (t : Finset ι) (f : ι → Set α) (g : ι → α),
  (∀ i ∈ t, g i ∈ f i) → ∑ i ∈ t, g i ∈ ∑ i ∈ t, f i

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

Assumes

AddCommMonoid