Definition is_z_isomorphism_path {C : category} {x y : C} {f f' : x --> y} (p : f = f') (Hf : is_z_isomorphism f) : is_z_isomorphism f'. Proof. use make_is_z_isomorphism. - exact (inv_from_z_iso (_ ,, Hf)). - split. + abstract (rewrite <- p ; apply (z_iso_inv_after_z_iso (_ ,, Hf))). + abstract (rewrite <- p ; apply (z_iso_after_z_iso_inv (_ ,, Hf))). Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories.