proposition: Lemma equiv_to_adjequiv_isadj : left_adjoint_axioms equiv_to_adjequiv_d.
proof: Proof. split ; cbn. - refine (maponpaths (fun z => ((z • _) • _) • _) (!help3) @ _). rewrite !vassocr. rewrite !(maponpaths (fun z => _ o (_ o z)) (!(vassocr _ _ _))). rewrite lassociator_rassociator, id2_right. rewrite !(maponpaths (fun z => _ o z) (!(vassocr _ _ _))). rewrite lwhisker_vcomp. rewrite vcomp_linv. rewrite lwhisker_id2. rewrite id2_right. rewrite rinvunitor_runitor. reflexivity. - rewrite <- !vassocr. exact first_triangle_law. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.Univalence