proposition: Lemma triangle_id_inverse (a : A) : z_iso_inv_from_z_iso (functor_on_z_iso F (eta a)) = eps (F a).
proof: 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.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core