Definition transportb_disp_ob2_mor_path {C₁ C₂ : category} {D : twosided_disp_cat C₁ C₂} {x x' : C₁} (p : x = x') {y y' : C₂} (q : y = y') (xy : D x' y') : transportf (λ z, D z y') p (transportf (λ z, D x z) q (transportb_disp_ob2 p q xy)) = xy. Proof. induction p, q. cbn. apply idpath. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness.