Lemma isweq_iso_from_iso_in_sub (a b : ob (full_sub_category C C')): isweq (iso_from_iso_in_sub a b). Proof. apply (isweq_iso _ (iso_in_sub_from_iso a b)). - intro f. apply z_iso_eq; simpl. apply eq_in_sub_precategory, idpath. - intro f; apply z_iso_eq, idpath. 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.