∀ {P : TopCat → Prop} (R : Type (max u_1 u_2)) [inst : Ring R] (X : ModuleCat R) (X_1 : (CompHausLike P)ᵒᵖ),
  ModuleCat.ofHom (LocallyConstant.comapₗ R (TopCat.Hom.hom (CategoryTheory.CategoryStruct.id X_1).unop.hom)) =
    CategoryTheory.CategoryStruct.id
      (match X_1 with
      | Opposite.op S => ModuleCat.of R (LocallyConstant ↑S.toTop ↑X))