proposition: Lemma dirprod_disp_cat_is_univalent : is_univalent_disp D1 → is_univalent_disp D2 → is_univalent_disp dirprod_disp_cat.
proof: Proof. intros HD1 HD2. apply is_univalent_disp_from_fibers. intros x xx xx'. use isweqhomot. - apply z_iso_disp_aux_weq. + apply is_univalent_in_fibers_from_univalent_disp. apply HD1. + apply is_univalent_in_fibers_from_univalent_disp. apply HD2. - intros p. induction p. cbn. apply (@eq_z_iso_disp _ dirprod_disp_cat). reflexivity. - apply z_iso_disp_aux_weq. 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