proposition: Lemma eqweq_ob_path_is_functor_app {A B : precategory_data} (F : catiso A B) : forall a : A, eqweqmap (catiso_to_precategory_ob_path F) a = F a.
proof: Proof. intros a. exact (! toforallpaths (λ _ : A, B) F (pr1 (eqweqmap (invmap (univalence A B) (catiso_ob_weq F)))) (maponpaths pr1 (! homotweqinvweq (univalence A B) (catiso_ob_weq F))) a). Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful