∀ {R : Type u} [inst : Semiring R] {ι : Type v} [dec_ι : DecidableEq ι] {M : Type u_1} [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] (A : ι → Submodule R M),
  DirectSum.coeLinearMap A = DirectSum.toModule R ι M fun i => (A i).subtype