proposition: Lemma inverse_is_inverse_1 a b (f : a --> b) : inverse (#F f) = f.
proof: Proof. unfold inverse. set (H' := nat_trans_ax (adjunit (pr1 H))). simpl in H'; rewrite <- H'; clear H'; simpl in *. rewrite <- assoc. intermediate_path (f · identity _). apply maponpaths. set (H' := z_iso_inv_after_z_iso (eta b)). apply H'. rewrite id_right. apply idpath. 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