Definition is_disp_invertible_2cell_runitor {B : bicat} {x y : B} {f : x --> y} {D : disp_bicat B} {xx : D x} {yy : D y} (ff : xx -->[f] yy) : is_disp_invertible_2cell (is_invertible_2cell_runitor f) (disp_runitor ff). Proof. use tpair. - exact (disp_rinvunitor ff). - split. + etrans. { apply disp_runitor_rinvunitor. } apply (transportf_paths (λ p, _ ==>[p] _)). apply B. + etrans. { apply disp_rinvunitor_runitor. } apply (transportf_paths (λ p, _ ==>[p] _)). apply B. 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.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Invertible_2cells.