-(* teorema di prova che non compila per via del let *)
-theorem le_gen_S_x_2: \forall m,x. (le (S m) x) \to let k \def (S O) in
- (\exists n. x = (S n) \land (le m n) \land k = k).
-intros.
-lapply le_gen_S_x to H using H0. elim H0. elim H1.
-exists. exact x1. auto.
-qed.
-
-(* proof of le_gen_S_S with lapply *)
-theorem le_gen_S_S_2: \forall m,n. (le (S m) (S n)) \to (le m n).
-intros.
-lapply le_gen_S_x_2 to H using H0. elim H0. elim H1.
-lapply eq_gen_S_S to H2 using H4. rewrite left H4. assumption.
-qed.
\ No newline at end of file
+(*
+theorem le_trans: \forall x,y. (le x y) \to \forall z. (le y z) \to (le x z).
+intros 1. elim x; clear H. clear x.
+auto paramodulation.
+fwd H1 [H]. decompose H.
+*)