simple induction l; simpl in |- *; intros; auto with arith pts.
Qed.
Hint Resolve beta_app_list_ctxt: pts.

Lemma beta_whnf_rec :
forall (e : env) (t : term) (args : list term),
sn (ctxt beta) e (app_list args t) ->
{u : term | red beta e (app_list args t) u &  head_normal beta e u}.