proposition: 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: Proof. rewrite Id_in_sub_to_iso_equal_iso. apply (twooutof3c _ idtoiso). apply pr2. apply H. 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