proposition: Proposition are_conjoints_left' {B : verity_double_bicat} {x y : B} {h : x --> y} {v : y -|-> x} (c : are_conjoints h v) : counit_are_conjoints c ⋆v unit_are_conjoints c = linvunitor _ ▹s (runitor _ ◃s id_h_square_bicat _).
proof: Proof. rewrite <- (are_conjoints_left c). rewrite !rwhisker_lwhisker_square. rewrite <- lwhisker_square_comp. rewrite runitor_rinvunitor. rewrite lwhisker_square_id. rewrite <- rwhisker_square_comp. rewrite lunitor_linvunitor. rewrite rwhisker_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