Definition trivial_disp_invertible_to_invertible_2cell {B C : bicat} {b₁ b₂ : B} {f : B ⟦ b₁, b₂ ⟧} {c₁ : trivial_displayed_bicat B C b₁} {c₂ : trivial_displayed_bicat B C b₂} {ff gg : c₁ -->[ f] c₂} : disp_invertible_2cell (id2_invertible_2cell f) ff gg → invertible_2cell ff gg. Proof. intros α. use make_invertible_2cell. - exact (pr1 α). - use (trivial_is_disp_invertible_to_is_invertible_2cell (is_invertible_2cell_id₂ f)). apply α. 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.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.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.