Lemma idtoiso_precompose_iso (C : category) (a a' b : ob C) (p : a = a') (f : z_iso a b) : z_iso_comp (idtoiso (!p)) f = transportf (λ a, z_iso a b) p f. Proof. destruct p. apply z_iso_eq. apply id_left. Qed.
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.