Lemma is_nat_trans_inv_from_pointwise_inv (C : precategory_data)(D : precategory) (hs: has_homsets D) (F G : ob [C,D,hs]) (A : F --> G) (H : is_nat_iso A) : is_nat_trans _ _ (λ a : ob C, inv_from_iso (tpair _ _ (H a))). Proof. apply is_nat_trans_inv_from_pointwise_inv_ext. exact hs. Qed.
Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence.