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