proposition: Proposition are_companions_left' {B : verity_double_bicat} {x y : B} {h : x --> y} {v : x -|-> y} (c : are_companions h v) : counit_are_companions c ⋆v unit_are_companions c = rinvunitor _ ▹s (lunitor _ ◃s id_h_square_bicat _).
proof: Proof. rewrite <- (are_companions_left c). rewrite !rwhisker_lwhisker_square. rewrite <- lwhisker_square_comp. rewrite lunitor_linvunitor. rewrite lwhisker_square_id. rewrite <- rwhisker_square_comp. rewrite runitor_rinvunitor. 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.Examples.TransposeDoubleBicat