Definition indexed_cat_comp_z_iso {C : category} (Φ : indexed_cat C) {x y z : C} (f : x --> y) (g : y --> z) (xx : Φ x) : z_iso ((Φ $ g) ((Φ $ f) xx)) ((Φ $ (f · g)) xx). Proof. refine (indexed_cat_comp Φ f g xx ,, _). apply is_z_isomorphism_indexed_cat_comp. Defined.
Require Import UniMath.MoreFoundations.All. 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.