Definition assoc_two_disp_alt {D : twosided_disp_cat} {x₁ x₂ x₃ x₄ : C₁} {y₁ y₂ y₃ y₄ : C₂} {xy₁ : D x₁ y₁} {xy₂ : D x₂ y₂} {xy₃ : D x₃ y₃} {xy₄ : D x₄ y₄} {f₁ : x₁ --> x₂} {f₂ : x₂ --> x₃} {f₃ : x₃ --> x₄} {g₁ : y₁ --> y₂} {g₂ : y₂ --> y₃} {g₃ : y₃ --> y₄} (fg₁ : xy₁ -->[ f₁ ][ g₁ ] xy₂) (fg₂ : xy₂ -->[ f₂ ][ g₂ ] xy₃) (fg₃ : xy₃ -->[ f₃ ][ g₃ ] xy₄) : ((fg₁ ;;2 fg₂) ;;2 fg₃) = transportf_disp_mor2 (assoc _ _ _) (assoc _ _ _) (fg₁ ;;2 (fg₂ ;;2 fg₃)).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.