Definition iso_in_sub_from_iso (a b : ob (full_sub_category C C')) (f : z_iso (pr1 a) (pr1 b)) : z_iso a b := tpair _ _ (iso_in_precat_is_iso_in_subcat a b f).
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.