∀ (R : Type u_2) {ι : Type u_3} [inst : Ring R] [inst_1 : Fintype ι] [inst_2 : DecidableEq ι] (M : Type u_1)
  [inst_3 : AddCommGroup M] [inst_4 : Module (Matrix ι ι R) M] (i : ι) (x y : M),
  (↑(DistribSMul.toAddMonoidHom M (Matrix.single i i 1))).toFun (x + y) =
    (↑(DistribSMul.toAddMonoidHom M (Matrix.single i i 1))).toFun x +
      (↑(DistribSMul.toAddMonoidHom M (Matrix.single i i 1))).toFun y