Proposition transport_f_f_disp_mor2 {D : twosided_disp_cat_data} {x₁ x₂ : C₁} {y₁ y₂ : C₂} {xy₁ : D x₁ y₁} {xy₂ : D x₂ y₂} {f₁ f₂ f₃ : x₁ --> x₂} (p₁ : f₁ = f₂) (p₂ : f₂ = f₃) {g₁ g₂ g₃ : y₁ --> y₂} (q₁ : g₁ = g₂) (q₂ : g₂ = g₃) (fg : xy₁ -->[ f₁ ][ g₁ ] xy₂) : transportf_disp_mor2 p₂ q₂ (transportf_disp_mor2 p₁ q₁ fg) = transportf_disp_mor2 (p₁ @ p₂) (q₁ @ q₂) fg. Proof. induction p₁, p₂, q₁, q₂ ; cbn. apply idpath. Qed.
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.