Definition pentagon_law {C : category} {D : twosided_disp_cat C C} {Cm : hor_comp D} (a : double_cat_associator Cm) : UU := ∏ (v w x y z : C) (h₁ : D v w) (h₂ : D w x) (h₃ : D x y) (h₄ : D y z), transportb_disp_mor2 (id_right _) (id_right _) (double_associator a h₁ h₂ (double_hor_comp Cm h₃ h₄) ;;2 double_associator a (double_hor_comp Cm h₁ h₂) h₃ h₄) = double_hor_comp_mor Cm (id_two_disp _) (double_associator a h₂ h₃ h₄) ;;2 double_associator a h₁ (double_hor_comp Cm h₂ h₃) h₄ ;;2 double_hor_comp_mor Cm (double_associator a h₁ h₂ h₃) (id_two_disp _).
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.