Proposition transportb_disp_mor2_eq {D : twosided_disp_cat} {x₁ x₂ : C₁} {y₁ y₂ : C₂} {xy₁ : D x₁ y₁} {xy₂ : D x₂ y₂} {f f' : x₁ --> x₂} {p p' : f' = f} {g g' : y₁ --> y₂} {q q' : g' = g} {fg fg' : xy₁ -->[ f ][ g ] xy₂} (s : fg = fg') : transportb_disp_mor2 p q fg = transportb_disp_mor2 p' q' fg'. Proof. assert (p = p') as h₁. { apply homset_property. } assert (q = q') as h₂. { apply homset_property. } rewrite h₁, h₂, s. 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.