proposition: Lemma roundtrip2_iso_z_iso {C : category} {b c : C} (f: z_iso b c) : iso_to_z_iso (z_iso_to_iso f) = f.
proof: Proof. destruct f as [f H]. use total2_paths_f. - apply idpath. - apply isaprop_is_z_isomorphism. Qed.
imports: UniMath.Foundations.PartA UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories