intros.
simpl in |- *.
apply lt_S_n.
apply le_lt_trans with (weight_gamma (b :: gamma)); try assumption.
simpl in |- *.
apply lt_le_S.
apply plus_lt_compat_r.
assumption.
Qed.

(* Specifications: *)
Lemma weight_gamma_weak' :
forall (a b : form) (gamma : flist) (n : nat),
weight a < weight b ->
weight b + weight_gamma gamma < S n -> weight a + weight_gamma gamma < n.