∀ {I : Type u} {α : Type u_1} {β : Type u_2} [inst : Monoid α] [inst_1 : AddMonoid β] [inst_2 : DistribMulAction α β]
  [inst_3 : DecidableEq I] (i : I) (r : α) (x : β), Pi.single i (r • x) = r • Pi.single i x