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

(* Specifications: *)
Lemma weight_gamma_weak3' :
forall (a b c d : form) (gamma : flist) (n : nat),
weight a + weight b + weight c < weight d ->
weight d + weight_gamma gamma < S n ->
weight a + (weight b + (weight c + weight_gamma gamma)) < n.