∀ (R : Type u_3) {ι : Type u_1} [inst : Ring R] [inst_1 : Fintype ι] [inst_2 : DecidableEq ι]
  (M : ModuleCat (Matrix ι ι R)) (j : ι) (x x_1 : ↑M),
  (fun i => ⟨Matrix.single j i 1 • (x + x_1), ⋯⟩) =
    (fun i => ⟨Matrix.single j i 1 • x, ⋯⟩) + fun i => ⟨Matrix.single j i 1 • x_1, ⋯⟩