Lemma double_transport_idtoiso (C : precategory) (a a' b b' : ob C) (p : a = a') (q : b = b') (f : a --> b) : double_transport p q f = inv_from_z_iso (idtoiso p) · f · idtoiso q. Proof. destruct p. destruct q. intermediate_path (identity _ · f). - apply pathsinv0; apply id_left. - apply pathsinv0; apply id_right. Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos.