Definition make_are_companions {B : verity_double_bicat} {x y : B} (h : x --> y) (v : x -|-> y) (φ : square_double_bicat h (id_h y) v (id_v y)) (ψ : square_double_bicat (id_h x) h (id_v x) v) (p : runitor _ ▹s (linvunitor _ ◃s ψ ⋆v φ) = id_h_square_bicat _) (q : runitor _ ▿s (linvunitor _ ▵s ψ ⋆h φ) = id_v_square_bicat _) : are_companions h v := φ ,, ψ ,, p ,, q.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.DerivedLaws. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.CellsAndSquares. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.UnderlyingCats. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.LocalUnivalence. Require Import UniMath.Bicategories.DoubleCategories.Examples.TransposeDoubleBicat.