Lemma isweq_Id_in_sub_to_iso (a b : ob (full_sub_category C C')) (H : is_univalent C) : isweq (Id_in_sub_to_iso a b). Proof. rewrite Id_in_sub_to_iso_equal_iso. apply (twooutof3c _ idtoiso). apply pr2. apply H. 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.