Definition binprod_cone_in_disp_map_slice : @binprod_cone (disp_map_slice_bicat D b) ff gg. Proof. use make_binprod_cone. - refine (pb ,, π₁ · f ,, _). apply D_comp. + exact (pb_preserves_pred_ob D Hg (mirror_has_pb_ump Hpb)). + exact Hf. - refine (π₁ ,, _ ,, _) ; cbn. + apply D_comp. * exact (pb_preserves_pred_ob D Hg (mirror_has_pb_ump Hpb)). * exact Hf. + exact (id2_invertible_2cell (π₁ · f)). - refine (π₂ ,, _ ,, _) ; cbn. + use (invertible_pred_mor_1 D (inv_of_invertible_2cell γ)). apply D_comp. * exact (pb_preserves_pred_ob D Hf Hpb). * exact Hg. + exact γ. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayMapBicatSlice. Require Import UniMath.Bicategories.Limits.Final. Require Import UniMath.Bicategories.Limits.Products. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.Examples.OpCellBicatLimits. Require Import UniMath.Bicategories.Logic.DisplayMapBicat.