Definition triangle_law {C : category} {D : twosided_disp_cat C C} {I : hor_id D} {Cm : hor_comp D} (l : double_cat_lunitor I Cm) (r : double_cat_runitor I Cm) (a : double_cat_associator Cm) : UU := ∏ (x y z : C) (h : D x y) (k : D y z), double_associator a h _ k ;;2 double_hor_comp_mor Cm (double_runitor r h) (id_two_disp _) = transportb_disp_mor2 (id_left _) (id_left _) (double_hor_comp_mor Cm (id_two_disp _) (double_lunitor l k)).
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.