proposition: Proposition are_conjoints_right' {B : verity_double_bicat} {x y : B} {h : x --> y} {v : y -|-> x} (c : are_conjoints h v) : unit_are_conjoints c ⋆h counit_are_conjoints c = linvunitor _ ▿s (runitor _ ▵s id_v_square_bicat _).
proof: Proof. rewrite <- (are_conjoints_right c). rewrite !dwhisker_uwhisker_square. rewrite <- uwhisker_square_comp. rewrite runitor_rinvunitor. rewrite uwhisker_square_id. rewrite <- dwhisker_square_comp. rewrite lunitor_linvunitor. rewrite dwhisker_square_id. apply idpath. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat UniMath.Bicategories.DoubleCategories.DoubleBicat.DerivedLaws UniMath.Bicategories.DoubleCategories.DoubleBicat.CellsAndSquares UniMath.Bicategories.DoubleCategories.DoubleBicat.UnderlyingCats UniMath.Bicategories.DoubleCategories.DoubleBicat.LocalUnivalence UniMath.Bicategories.DoubleCategories.DoubleBicat.CompanionPairs UniMath.Bicategories.DoubleCategories.DoubleBicat.CompanionPairUnique UniMath.Bicategories.DoubleCategories.Examples.HorizontalDual