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