proposition: Lemma nat_trans_inv_pointwise_inv_after_p (C : precategory_data) (C' : precategory) (hs: has_homsets C') (F G : ob [C, C', hs]) (A : F --> G) (Aiso: is_iso A) a : inv_from_iso (functor_iso_pointwise_if_iso C C' hs F G A Aiso a) = pr1 (inv_from_iso (make_iso A Aiso)) a.
proof: Proof. apply pathsinv0. apply inv_iso_unique'. unfold precomp_with. simpl. set (TA := iso_inv_after_iso (make_iso A Aiso)). simpl in TA. apply (nat_trans_eq_pointwise TA). 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