∀ {ι : Type u_2} {R : Type u_3} {A : Type u_1} [inst : DecidableEq ι] [inst_1 : AddMonoid ι] [inst_2 : CommSemiring R]
  [inst_3 : Semiring A] [inst_4 : Algebra R A] (𝒜 : ι → Submodule R A) [i : GradedAlgebra 𝒜],
  Function.RightInverse (⇑(DirectSum.coeAddMonoidHom 𝒜)) DirectSum.Decomposition.decompose'