proposition: Lemma disp_full_sub_univalent (C : category) (P : C → UU) : (∏ x : C, isaprop (P x)) → is_univalent_disp (disp_full_sub C P).
proof: Proof. intro HP. apply is_univalent_disp_from_fibers. intros x xx xx'. cbn in *. apply isweqcontrprop. apply HP. apply isofhleveltotal2. - apply isapropunit. - intro. apply (@isaprop_is_z_iso_disp _ (disp_full_sub C P)). Defined.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Examples.Reindexing