proposition: Proposition duality_involution_inv_of_2cell_psfunctor_eq {x y : B} {f g : x --> y} (τ : g ==> f) : duality_involution_inv_of_2cell (## L τ) = τ.
proof: Proof. unfold duality_involution_inv_of_2cell. simpl. rewrite !vassocl. use vcomp_move_R_pM ; [ is_iso | ]. simpl. rewrite <- vcomp_runitor. rewrite !vassocr. apply maponpaths_2. rewrite !vassocl. etrans. { do 2 apply maponpaths. rewrite !vassocr. do 2 apply maponpaths_2. rewrite !rwhisker_vcomp. apply maponpaths. rewrite !vassocl. etrans. { apply maponpaths. exact (psnaturality_natural η _ _ _ _ τ). } rewrite !vassocr. rewrite vcomp_linv. apply id2_left. } etrans. { apply maponpaths. rewrite !vassocr. rewrite rwhisker_rwhisker. rewrite !vassocl. apply maponpaths. rewrite !vassocr. rewrite lassociator_rassociator. rewrite id2_left. apply idpath. } rewrite !vassocr. rewrite <- vcomp_whisker. rewrite !vassocl. rewrite lwhisker_vcomp. refine (_ @ id2_right _). apply maponpaths. rewrite <- lwhisker_id2. apply maponpaths. exact (vcomp_rinv (invertible_modcomponent_of (unit_unit_inv_of_duality HL) y)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.UnivalenceOp UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Morphisms.FullyFaithful UniMath.Bicategories.Morphisms.Properties.ContainsAdjEquiv UniMath.Bicategories.Core.EquivToAdjequiv UniMath.Bicategories.Core.Examples.OpCellBicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.PseudoFunctors.Properties UniMath.Bicategories.PseudoFunctors.Examples.Identity UniMath.Bicategories.PseudoFunctors.Examples.Composition UniMath.Bicategories.PseudoFunctors.Examples.Op2OfPseudoFunctor UniMath.Bicategories.PseudoFunctors.Examples.OpFunctor UniMath.Bicategories.Transformations.PseudoTransformation UniMath.Bicategories.Transformations.Examples.Associativity UniMath.Bicategories.Transformations.Examples.Unitality UniMath.Bicategories.Transformations.Examples.Whiskering UniMath.Bicategories.Modifications.Modification UniMath.Bicategories.OtherStructure.DualityInvolution