proposition: Lemma isweq_sub_precat_paths_to_iso (a b : ob (full_sub_category C C')) (H : is_univalent C) : isweq (@idtoiso _ a b).
proof: Proof. rewrite precat_paths_in_sub_as_3_maps. match goal with |- isweq (funcomp ?f ?g) => apply (twooutof3c f g) end. - apply isweq_Id_in_sub_to_iso; assumption. - apply isweq_iso_in_sub_from_iso. Defined.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Subcategory.Core