trivial.
trivial.
intros; simpl in |- *.
apply le_n_S.
apply le_O_n.
intros a ih_a b ih_b.
clear ih_a ih_b.
case a; clear a; intros; simpl in |- *; apply le_n_S; apply le_O_n.
intros a ih_a b ih_b.
simpl in |- *.
fold weight_neg in |- *.
apply le_trans with (weight b); try assumption.
apply (plus_le_compat_r 0 (weight_neg a) (weight b)).
apply le_O_n.
Qed.

Lemma weight_neg_le :
forall (j : Int) (a : form),
weight_neg (Imp (Atom j) a) <= S (S (S (weight_neg a))).