proposition: Lemma Convn_weak n m (u : 'I_m -> 'I_n) (d : {fdist 'I_m}) (g : 'I_n -> T) : <|>_d (g \o u) = <|>_(fdistmap u d) g.
proof: Proof. apply S1_inj. rewrite !S1_Convn (partition_big u (fun _=> true)) //=. apply eq_bigr => i _. rewrite fdistmapE /=. have HF (a : 'I_m) : (0 <= d a)%coqR. by []. rewrite (@scalept_sum _ _ _ (mkNNFun HF)) /=. by apply eq_bigr => a /eqP ->. 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