Definition comp_are_conjoints {B : verity_double_bicat} {x y z : B} {h₁ : x --> y} {h₂ : y --> z} {v₁ : y -|-> x} {v₂ : z -|-> y} (c₁ : are_conjoints h₁ v₁) (c₂ : are_conjoints h₂ v₂) : are_conjoints (h₁ · h₂) (v₂ · v₁). Proof. exact (comp_are_companions (B := horizontal_dual_verity_double_bicat B) c₂ c₁). Defined.
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.DoubleBicat.CompanionPairs. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.CompanionPairUnique. Require Import UniMath.Bicategories.DoubleCategories.Examples.HorizontalDual.