∀ {M : Type u_1} [inst : AddMonoid M] (S : AddSubgroup (AddUnits M)),
  S.ofAddUnitsEquivType =
    { toFun := fun x => ⟨S.addUnit_of_mem_ofAddUnits ⋯, ⋯⟩, invFun := fun x => ⟨↑↑x, ⋯⟩, left_inv := ⋯, right_inv := ⋯,
      map_add' := ⋯ }