| le_succ: \forall m, n. (le m n) \to (le (S m) (S n)).
theorem le_refl: \forall x. (le x x).
-intros. elim x. auto paramodulation. auto paramodulation.
+intros. elim x; auto new.
qed.
theorem le_gen_x_O_aux: \forall x, y. (le x y) \to (y =O) \to
qed.
theorem le_gen_x_O_cc: \forall x. (x = O) \to (le x O).
-intros. elim H. auto paramodulation.
+intros. elim H. auto new.
qed.
theorem le_gen_S_x_aux: \forall m,x,y. (le y x) \to (y = S m) \to
(\exists n. x = (S n) \land (le m n)).
intros 4. elim H.
apply eq_gen_S_O. exact m. elim H1. auto paramodulation.
-cut (n = m). elim Hcut. apply ex_intro. exact n1. auto paramodulation. auto new. (* paramodulation non trova la prova *)
+cut (n = m). elim Hcut. apply ex_intro. exact n1. auto new.auto paramodulation.
qed.
theorem le_gen_S_x: \forall m,x. (le (S m) x) \to
theorem le_gen_S_x_cc: \forall m,x. (\exists n. x = (S n) \land (le m n)) \to
(le (S m) x).
-intros. elim H. elim H1. cut ((S x1) = x). elim Hcut. auto paramodulation. elim H2. auto paramodulation.
+intros. elim H. elim H1. cut ((S x1) = x). elim Hcut. auto new.
+elim H2. auto paramodulation.
qed.
theorem le_gen_S_S: \forall m,n. (le (S m) (S n)) \to (le m n).
intros.
-lapply le_gen_S_x to H using H0. elim H0. elim H1.
-lapply eq_gen_S_S to H2 using H4. rewrite > H4. assumption.
+lapply le_gen_S_x to H as H0. elim H0. elim H1.
+lapply eq_gen_S_S to H2 as H4. rewrite > H4. assumption.
qed.
theorem le_gen_S_S_cc: \forall m,n. (le m n) \to (le (S m) (S n)).
-intros. auto paramodulation.
+intros. auto new.
qed.
(*