Definition two_disp_pre_whisker_right {D : twosided_disp_cat} {x₁ x₂ x₃ : C₁} {y₁ y₂ y₃ : C₂} {xy₁ : D x₁ y₁} {xy₂ : D x₂ y₂} {xy₃ : D x₃ y₃} {f₁ : x₁ --> x₂} {f₂ : x₂ --> x₃} {g₁ g₁' : y₁ --> y₂} (p : g₁' = g₁) {g₂ : y₂ --> y₃} (fg₁ : xy₁ -->[ f₁ ][ g₁' ] xy₂) (fg₂ : xy₂ -->[ f₂ ][ g₂ ] xy₃) : transportf (λ z, _ -->[ _ ][ z ] _) p fg₁ ;;2 fg₂ = transportf (λ z, _ -->[ _ ][ z ] _) (maponpaths (λ z, z · _) p) (fg₁ ;;2 fg₂).
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.