Lemma transportf_isotoid (C : category) (H : is_univalent C) (a a' b : ob C) (p : z_iso a a') (f : a --> b) : transportf (λ a0 : C, a0 --> b) (isotoid C H p) f = inv_from_z_iso p · f. Proof. rewrite <- idtoiso_precompose. rewrite idtoiso_inv. rewrite idtoiso_isotoid. apply idpath. 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.