Ltac des := 
    match goal with
      | [H : exists _, _ |- _] => destruct H
    end.

(* Specifications: *)
Theorem polynomial_const : forall c, polynomial (fun n => c).
Theorem polynomial_ident : polynomial (fun n => n).
Theorem polynomial_mult : forall f1 f2 , polynomial f1 -> polynomial f2 -> polynomial (fun n => f1 n * f2 n).