+
+alias id "le" = "cic:/matita/dama/ordered_set/le.con".
+lemma os_le_to_nat_le:
+ ∀a,b:nat_ordered_set.le nat_ordered_set a b → a ≤ b.
+intros; normalize in H; apply (not_lt_to_le ?? H);
+qed.
+
+lemma nat_le_to_os_le:
+ ∀a,b:nat_ordered_set.a ≤ b → le nat_ordered_set a b.
+intros 3; apply (le_to_not_lt a b);assumption;
+qed.
+
\ No newline at end of file