Definition prod_of_twosided_disp_cat_id_comp : twosided_disp_cat_id_comp prod_of_twosided_disp_cat_ob_mor. Proof. simple refine (_ ,, _). - exact (λ x y xy, id_two_disp (pr1 xy) ,, id_two_disp (pr2 xy)). - exact (λ x₁ x₂ x₃ y₁ y₂ y₃ xy₁ xy₂ xy₃ f₁ f₂ g₁ g₂ fg₁ fg₂, (pr1 fg₁ ;;2 pr1 fg₂) ,, (pr2 fg₁ ;;2 pr2 fg₂)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete.