proposition: Lemma is_nat_trans_inv_from_pointwise_inv_ext {C : precategory_data} {D : precategory} (hs: has_homsets D) {F G : functor_data C D} {A : nat_trans F G} (H : is_nat_iso A) : is_nat_trans _ _ (λ a : ob C, inv_from_iso (tpair _ _ (H a))).
proof: Proof. red. intros x x' f. apply pathsinv0. apply iso_inv_on_right. rewrite assoc. apply iso_inv_on_left. set (HA:= pr2 A). simpl in *. apply pathsinv0. unfold is_nat_trans in HA. apply HA. Qed.
imports: UniMath.Foundations.Propositions UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Univalence UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence