proposition: Lemma functor_iso_if_pointwise_iso (C : precategory_data) (C' : precategory) (hs: has_homsets C') (F G : ob [C, C', hs]) (A : F --> G) : is_nat_iso A -> is_iso A .
proof: Proof. intro H. apply (is_iso_qinv _ (nat_trans_inv_from_pointwise_inv _ _ _ _ _ _ H)). simpl; apply is_inverse_nat_trans_inv_from_pointwise_inv. Defined.
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