Lemma isweq_sub_precat_paths_to_iso (a b : ob (full_sub_category C C')) (H : is_univalent C) : isweq (@idtoiso _ a b). 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.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Subcategory.Core.