(** * Multiplication of a list of expressions  - with any arities: (n,0) *)
Fixpoint multl_e (n:nat)(el:list BC) : BC :=
match el with
| nil => one_e n 0
| e' :: el' => comp n 0 mult_e [e'; multl_e n el'] nil
end.

(* Specifications: *)
Lemma multl_arities :
forall el n,
andl (fun e => arities e = ok_arities n 0) el ->
arities (multl_e n el) = ok_arities n 0.