(** * Some properties of [cond] *)

Lemma cond_simpl_notnil n s fn fc ft ff l1 l2 :
sem fc l1 l2 <> nil ->
sem (comp n s cond nil [fc; fn; ft; ff]) l1 l2 =
match sem fc l1 l2 with
| nil => nil
| true :: _ => sem ft l1 l2
| false :: _ => sem ff l1 l2
end.