Definition double_runitor_laws {C : category} {D : twosided_disp_cat C C} {I : hor_id D} {Cm : hor_comp D} (r : double_runitor_data I Cm) : UU := ∏ (x₁ x₂ y₁ y₂ : C) (h₁ : D x₁ y₁) (h₂ : D x₂ y₂) (v₁ : x₁ --> x₂) (v₂ : y₁ --> y₂) (τ : h₁ -->[ v₁ ][ v₂ ] h₂), transportb_disp_mor2 (id_right _ @ !(id_left _)) (id_right _ @ !(id_left _)) (r _ _ h₁ ;;2 τ) = double_hor_comp_mor Cm τ (double_id_mor I _) ;;2 r _ _ h₂.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos.