Definition disp_bifunctor_leftcompax {A B C : category} {F : bifunctor A B C} {DA : disp_cat A} {DB : disp_cat B} {DC : disp_cat C} (DF : disp_bifunctor_data F DA DB DC) : UU := ∏ (x : A) (y1 y2 y3 : B) (g1 : B⟦y1,y2⟧) (g2 : B⟦y2,y3⟧) (xx : DA x) (yy1 : DB y1) (yy2 : DB y2) (yy3 : DB y3) (gg1 : yy1 -->[g1] yy2) (gg2 : yy2 -->[g2] yy3), (xx ⊗⊗^{DF}_{l} (gg1 ;; gg2) = transportb _ (bifunctor_leftcomp F _ _ _ _ g1 g2) ((xx ⊗⊗^{DF}_{l} gg1) ;; (xx ⊗⊗^{DF}_{l} gg2))).
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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Core.Isos. Import BifunctorNotations. Import DisplayedBifunctorNotations.