∀ (P : TopCat → Prop) [inst : CompHausLike.HasExplicitFiniteCoproducts P] [inst_1 : CompHausLike.HasExplicitPullbacks P]
  (hs :
    ∀ ⦃X Y : CompHausLike P⦄ (f : X ⟶ Y),
      CategoryTheory.EffectiveEpi f → Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom f))
  (X : Type (max u_1 u_2)),
  { val := CompHausLike.LocallyConstant.functorToPresheaves.map (CategoryTheory.CategoryStruct.id X) } =
    CategoryTheory.CategoryStruct.id { val := CompHausLike.LocallyConstant.functorToPresheaves.obj X, cond := ⋯ }