proposition: 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: Proof. intro Hyp. induction d' as (c,(p,d)). destruct p. exact Hyp. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.StreetFibration