Lemma double_transport_idtodaggeriso (a a' b b' : pr111 D) (p : a = a') (q : b = b') (f : a --> b) : Univalence.double_transport p q f = pr1 (idtodaggeriso dagD _ _ (! p)) · f · pr1 (idtodaggeriso dagD _ _ q). Proof. destruct p. destruct q. intermediate_path (identity _ · f). - apply pathsinv0; apply id_left. - apply pathsinv0; apply id_right. Qed.
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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DaggerCategories.Categories. Require Import UniMath.CategoryTheory.DaggerCategories.Unitary. Require Import UniMath.CategoryTheory.DaggerCategories.Univalence. Require Import UniMath.CategoryTheory.DaggerCategories.Functors. Require Import UniMath.CategoryTheory.DaggerCategories.Transformations.