proposition: Lemma make_adj_equivalence_of_cats'_form_adjunction : form_adjunction F G make_adj_equivalence_of_cats'_unit make_adj_equivalence_of_cats'_counit.
proof: Proof. use make_form_adjunction. - intro a. refine (maponpaths (λ x, x · _) (functor_on_inv_from_z_iso _ _) @ _). apply z_iso_inv_on_right. symmetry. refine (id_right _ @ _). refine (_ @ id_right _). symmetry. apply z_iso_inv_on_right. symmetry. apply (pr2 H1). - intro a. refine (maponpaths _ (functor_on_inv_from_z_iso _ _) @ _). apply z_iso_inv_on_right. symmetry. refine (id_right _ @ _). refine (_ @ id_right _). symmetry. apply z_iso_inv_on_right. symmetry. apply (pr1 H1). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Adjunctions.Core