Lemma equiv_to_adjequiv_isadj : left_adjoint_axioms equiv_to_adjequiv_d. 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.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.