--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "nat/order.ma".
+include "datatypes/bool.ma".
+
+naxiom decompose1: ¬(lt O O).
+naxiom decompose2: ∀n. ¬(lt (S n) O).
+
+ndefinition ltb: nat → nat → bool.
+ #n; nelim n
+ [ #m; ncases m
+ [ napply false
+ | #m'; napply true ]
+##| #n'; #Hn'; #m; ncases m
+ [ napply false
+ | #m'; ncases (Hn' m')
+ [ napply true
+ | napply false]##]
+nqed.