proposition: Proposition eq_are_companions {B : verity_double_bicat} {x y : B} {h : x --> y} {v : x -|-> y} {c₁ c₂ : are_companions h v} (p : unit_are_companions c₁ = unit_are_companions c₂) (q : counit_are_companions c₁ = counit_are_companions c₂) : c₁ = c₂.
proof: Proof. use total2_paths_f. - exact p. - use subtypePath. { intro. apply isapropdirprod ; apply isaset_square_double_bicat. } rewrite pr1_transportf. rewrite transportf_const. exact q. 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