proposition: Lemma z_iso_disp_aux_weq (U1 : is_univalent_in_fibers D1) (U2 : is_univalent_in_fibers D2) (x : C) (xx xx' : D1 x × D2 x) : xx = xx' ≃ @z_iso_disp _ dirprod_disp_cat _ _ (identity_z_iso x) xx xx'.
proof: Proof. eapply weqcomp. apply pathsdirprodweq. apply invweq. eapply weqcomp. apply z_iso_disp_prod_weq. apply invweq. apply weqdirprodf. - exists idtoiso_fiber_disp. apply U1. - exists idtoiso_fiber_disp. apply U2. 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