Lemma roundtrip1_iso_z_iso {C : precategory} {b c : C} (f: iso b c) : z_iso_to_iso (iso_to_z_iso f) = f. Proof. destruct f as [f H]. use total2_paths_f. - apply idpath. - apply isaprop_is_iso. Qed.
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.