+interpretation "natural 'less or equal to'" 'leq x y = (le x y).
+interpretation "natural 'neither less nor equal to'" 'nleq x y = (Not (le x y)).
+
+ndefinition lt ≝ λn,m. S n ≤ m.
+
+interpretation "natural 'less than'" 'lt x y = (lt x y).
+interpretation "natural 'not less than'" 'nless x y = (Not (lt x y)).