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