update in basic_2

[helm.git] / helm / software / matita / nlibrary / nat / compare.ma

diff --git a/helm/software/matita/nlibrary/nat/compare.ma b/helm/software/matita/nlibrary/nat/compare.ma
index 2014d2aa4218d3ea35c6303b5a215ec5feb9dc45..354e61a5a3b80d479ca22835b5f96d2fd852f87d 100644 (file)
--- a/helm/software/matita/nlibrary/nat/compare.ma
+++ b/helm/software/matita/nlibrary/nat/compare.ma
@@ -18,14 +18,14 @@ include "datatypes/bool.ma".
 naxiom decompose1: ¬(lt O O).
 naxiom decompose2: ∀n. ¬(lt (S n) O).
 
-ndefinition ltb: ∀n,m:nat. lt n m ∨ ¬(lt n m).
+ndefinition ltb: nat → nat → bool.
  #n; nelim n
   [ #m; ncases m
-    [ napply or_intror; #H; napply (decompose1 H)
-    | #m'; napply or_introl; napply lt_O_Sn ]
+    [ napply false
+    | #m'; napply true ]
 ##| #n'; #Hn'; #m; ncases m
-    [ napply or_intror; #H; napply (decompose2 … H)
+    [ napply false
     | #m'; ncases (Hn' m')
-       [ #H; napply or_introl; napply le_S_S; napply H
-       | #H; napply or_intror; #K; napply H; napply le_S_S_to_le; napply K]##]
+       [ napply true
+       | napply false]##]
 nqed.