Definition disp_prebicat_of_univ_disp_cats_data : disp_prebicat_data bicat_of_univ_cats. Proof. exists disp_bicat_of_univ_disp_cats_1_id_comp_cells. repeat split. - intros ? ? ? ? ? F' ; cbn in *. exact (disp_nat_trans_id F'). - intros ? ? ? ? ? F' ; cbn in *. exact (disp_nat_trans_id F'). - intros ? ? ? ? ? F' ; cbn in *. exact (disp_nat_trans_id F'). - intros ? ? ? ? ? F' ; cbn in *. exact (disp_nat_trans_id F'). - intros ? ? ? ? ? F' ; cbn in *. exact (disp_nat_trans_id F'). - intros ? ? ? ? ? ? ? ? ? ? ? ? ? F' ; cbn in *. exact (disp_nat_trans_id (disp_functor_composite_data (disp_functor_composite ff gg) F')). - intros ? ? ? ? ? ? ? ? ? ? ? ? ? F' ; cbn in *. exact (disp_nat_trans_id (disp_functor_composite_data (disp_functor_composite ff gg) F')). - intros C D ? ? ? ? ? ? ? ? ? ? rr ss ; cbn in *. exact (@disp_nat_trans_comp C _ _ _ _ _ _ _ _ _ _ _ rr ss). - intros C₁ C₂ C₃ f g₁ g₂ r D₁ D₂ D₃ ff gg₁ gg₂ rr ; cbn in *. exact (@pre_whisker_disp_nat_trans C₁ C₂ _ _ _ _ _ _ _ _ _ _ _ rr). - intros C₁ C₂ C₃ ? ? ? ? ? ? ? ? ? ? rr ; cbn in *. exact (@post_whisker_disp_nat_trans C₁ C₂ _ _ _ _ _ _ _ _ _ _ rr _). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Adjunctions. Require Import UniMath.CategoryTheory.DisplayedCats.Equivalences. Require Import UniMath.CategoryTheory.DisplayedCats.DisplayedFunctorEq. Require Import UniMath.CategoryTheory.DisplayedCats.EquivalenceOverId. Require Import UniMath.CategoryTheory.DisplayedCats.DisplayedCatEq. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sigma. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat.