Lemma triangle_id_inverse (a : A) : z_iso_inv_from_z_iso (functor_on_z_iso F (eta a)) = eps (F a). Proof. apply z_iso_eq. simpl. match goal with | [ |- ?x = ?y ] => transitivity (x · identity _) end. apply pathsinv0, id_right. apply z_iso_inv_on_right. set (H' := triangle_id_left_ad (pr2 (pr1 H)) a). apply pathsinv0. apply H'. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core.