Definition local_opcartesian_trivial_comprehension : local_opcartesian_disp_psfunctor trivial_comprehension. Proof. intros b₁ b₂ f₁ f₂ α c₁ c₂ g₁ g₂ β Hβ ; cbn in *. apply is_opcartesian_2cell_sopfib_to_is_opcartesian_2cell ; cbn. apply invertible_to_opcartesian. refine (transportb is_invertible_2cell (pair_2cell_pr2 _ _ _) _). is_iso. - apply prod_1cell_pr2. - exact (trivial_opcartesian_2cell_is_invertible _ _ _ _ Hβ). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.Properties. Require Import UniMath.Bicategories.Morphisms.Properties.Projections. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.CartesianPseudoFunctor. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Trivial. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Codomain. Require Import UniMath.Bicategories.DisplayedBicats.ExamplesOfCleavings.TrivialCleaving. Require Import UniMath.Bicategories.DisplayedBicats.ExamplesOfCleavings.CodomainCleaving. Require Import UniMath.Bicategories.Limits.Products. Import Products.Notations. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.Logic.ComprehensionBicat.