∀ {ι : Type u_1} [inst : DecidableEq ι] (M : ι → Type u_2) [inst_1 : (i : ι) → AddCommMonoid (M i)] (M' : Type u_3)
  [inst_2 : AddCommMonoid M'] (φ ψ : ((i : ι) → M i) →+ M'),
  (fun i => (φ + ψ).comp (AddMonoidHom.single M i)) =
    (fun i => φ.comp (AddMonoidHom.single M i)) + fun i => ψ.comp (AddMonoidHom.single M i)