Proposition transport_b_b_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 : f₂ = f₁) (p₂ : f₃ = f₂) {g₁ g₂ g₃ : y₁ --> y₂} (q₁ : g₂ = g₁) (q₂ : g₃ = g₂) (fg : xy₁ -->[ f₁ ][ g₁ ] xy₂) : transportb_disp_mor2 p₂ q₂ (transportb_disp_mor2 p₁ q₁ fg) = transportb_disp_mor2 (p₂ @ p₁) (q₂ @ q₁) 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.