Lemma DF_inv_mor_simpl {DM DN: disp_functor H D' D''} {c':C'} {d':D' c'} (A: (DF ◦ DM) ↙d' ←d' -->[identity _] (DF ◦ DN) ↙d' ←d') (B: (DF ◦ DN) ↙d' ← d'-->[identity _] (DF ◦ DM) ↙d' ←d') : (A;;B = transportb _ (id_left _) (id_disp _)-> (DF_inv_mor DM DN c' d' A);;(DF_inv_mor DN DM c' d' B) = transportb _ (id_left _) (id_disp (DM c' d')))%mor_disp. Proof. intro Hyp. induction d' as (c,(p,d)). destruct p. exact Hyp. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.StreetFibration.