Lemma iso_stable_under_equalitytransportf {C : category} {x y z : C} {f : C⟦x,y⟧} {g : C⟦x,z⟧} {pf : y = z} (qg : g = transportf _ pf f) (Hf : is_z_isomorphism f) : is_z_isomorphism g. Proof. use (iso_stable_under_equality qg). use (iso_stable_under_transportf). exact Hf. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import BifunctorNotations. Import MonoidalNotations.