Definition disp_invertible_2cell_weq_along_iso_left (τ : disp_invertible_2cell (id2_invertible_2cell (# F f)) (disp_psfunctor_mor _ _ _ FF ff) (disp_psfunctor_mor _ _ _ FF gg)) : disp_invertible_2cell (id2_invertible_2cell f) ff gg. Proof. simple refine (_ ,, _ ,, _ ,, _). - refine (disp_psfunctor_iso_invmap_2 HF (transportb (λ z, _ ==>[ z ] _) _ (pr1 τ))). abstract (rewrite psfunctor_id2 ; apply idpath). - refine (disp_psfunctor_iso_invmap_2 HF (transportb (λ z, _ ==>[ z ] _) _ (pr12 τ))). abstract (cbn ; rewrite psfunctor_id2 ; apply idpath). - abstract (refine (disp_psfunctor_iso_invmap_2_vcomp _ _ _ @ _) ; unfold transportb ; rewrite disp_mor_transportf_prewhisker ; rewrite disp_mor_transportf_postwhisker ; rewrite !transport_f_f ; etrans ; [ do 3 apply maponpaths ; apply (pr2 τ) | ] ; unfold transportb ; rewrite transport_f_f ; rewrite disp_psfunctor_iso_invmap_2_id2 ; apply maponpaths_2 ; apply cellset_property). - abstract (refine (disp_psfunctor_iso_invmap_2_vcomp _ _ _ @ _) ; unfold transportb ; rewrite disp_mor_transportf_prewhisker ; rewrite disp_mor_transportf_postwhisker ; rewrite !transport_f_f ; etrans ; [ do 3 apply maponpaths ; apply (pr2 τ) | ] ; unfold transportb ; rewrite transport_f_f ; rewrite disp_psfunctor_iso_invmap_2_id2 ; apply maponpaths_2 ; apply cellset_property). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.Initial. Require Import UniMath.Bicategories.Core.Examples.Final. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.Bicategories.Core.AdjointUnique. 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.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor. Require Import UniMath.Bicategories.DisplayedBicats.DispTransportLaws.