proposition: Lemma transportf_precompose_disp {C} {D : disp_cat C} {c d : C} (f : c --> d ) {cc cc' : D c} (e : cc = cc') {dd} (ff : cc -->[f] dd) : transportf (λ xx : D c, xx -->[f] dd) e ff = transportf _ (id_left _) (z_iso_inv_from_z_iso_disp (idtoiso_disp (idpath _) (e)) ;; ff).
proof: Proof. destruct e; cbn. rewrite (@id_left_disp _ _ _ _ _ cc). apply pathsinv0, transportfbinv. Qed.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Core