proposition: Lemma ssum_perm n (F : 'I_n -> A) (pe : 'S_n) : \ssum_(i < n) F i = \ssum_(i < n) F (pe i).
proof: Proof. rewrite -!barycenter_map /barycenter big_map map_comp big_map. exact/perm_big/perm_eq_perm. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg fingroup perm matrix) mathcomp(mathcomp_extra boolp classical_sets Rstruct) mathcomp(ssrnum ereal) mathcomp(lra Rstruct reals) Reals ssrR Reals_ext Ranalysis_ext ssr_ext ssralg_ext logb realType_ext fdist