Lemma isotoid_2_1_id {B : bicat} (HB : is_univalent_2_1 B) {a b : B} (f : a --> b) : idpath f = isotoid_2_1 HB (id2_invertible_2cell f). Proof. use (invmaponpathsincl (idtoiso_2_1 _ _)). - apply isinclweq. exact (HB _ _ _ _). - rewrite idtoiso_2_1_isotoid_2_1. apply idpath. Qed.
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.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.