proposition: Lemma forms_cone_sigma_disp_cat (u v : vertex J) (e : edge u v) : compose (C := total_category sigma_disp_cat) (a := _ ,, _) (_ ,, cone_sigma_disp_cat u) (dmor d e) = (_ ,, cone_sigma_disp_cat v).
proof: Proof. apply (pr2 (mapcone E_to_sigma_total_functor _ (make_cone _ (pr221 HE)))). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Limits