Theorems · Theorem · group theory

Set.mem_finsetSum

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

The n-ary version of Set.mem_add.

Defined in

Mathlib.Algebra.Group.Pointwise.Set.BigOperators

Cited by

4 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoid