Definition disp_triangle_identity {C : category} {D : disp_cat C} {M : monoidal C} {DT : disp_tensor D M} {i : D I_{M}} (dlu : disp_leftunitor_data DT i) (dru : disp_rightunitor_data DT i) (dα : disp_associator_data DT) : UU := ∏ (x y : C) (xx : D x) (yy : D y), ((dα x I_{M} y xx i yy) ;; (xx ⊗⊗^{DT}_{l} dlu y yy )) = transportb _ ((monoidal_triangleidentity M) x y) ((dru x xx) ⊗⊗^{DT}_{r} yy).
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.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Projection. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Import MonoidalNotations. Import DisplayedBifunctorNotations.