proposition: Lemma sigma_lim_arrow_commutes : is_cone_mor d'_cone (make_cone _ forms_cone_sigma_disp_cat) sigma_lim_arrow.
proof: Proof. intro u. exact (maponpaths (# E_to_sigma_total_functor)%cat (limArrowCommutes d_cone _ e_cone u)). 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