Lemma transportf_isotoid_dep (C : precategory) (a a' : C) (p : a = a') (f : ∏ c, a --> c) : transportf (λ x : C, ∏ c, x --> c) p f = λ c, idtoiso (!p) · f c. Proof. destruct p. simpl. apply funextsec. intro. rewrite id_left. 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.