proposition: Lemma fdist_prod2_conv p (a b : fdist R A) : ((a <| p |> b) `X W)`2 = (a `X W)`2 <| p |> (b `X W)`2.
proof: Proof. apply/fdist_ext => b0. rewrite fdist_sndE fdist_convE !fdist_sndE 2!big_distrr /=. rewrite -big_split; apply eq_bigr => a0 _; rewrite !fdist_prodE fdist_convE /=. by rewrite mulrDl !mulrA. Qed.
imports: mathcomp(all_ssreflect ssralg fingroup perm matrix) mathcomp(all_algebra vector reals normedtype) mathcomp(mathcomp_extra boolp) mathcomp(Rstruct) ssrR logb realType_ext ssr_ext ssralg_ext bigop_ext