Definition id_two_disp_right {D : twosided_disp_cat} {x₁ x₂ : C₁} {y₁ y₂ : C₂} {xy₁ : D x₁ y₁} {xy₂ : D x₂ y₂} {f : x₁ --> x₂} {g : y₁ --> y₂} (fg : xy₁ -->[ f ][ g ] xy₂) : fg ;;2 id_two_disp xy₂ = transportb_disp_mor2 (id_right _) (id_right _) fg. Proof. exact (pr122 D _ _ _ _ _ _ _ _ fg). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.