S_pred moved from Z/times.ma to nat/orders.ma

[helm.git] / helm / matita / library / nat / orders.ma

diff --git a/helm/matita/library/nat/orders.ma b/helm/matita/library/nat/orders.ma
index d4979231d1d1d46a0b4a7cea579c086fef3bdb62..34cd6f6a3aa2adc7eeedf033616aa5b9d5ea79c5 100644 (file)
--- a/helm/matita/library/nat/orders.ma
+++ b/helm/matita/library/nat/orders.ma
@@ -83,6 +83,12 @@ apply H.assumption.
 apply le_S_S_to_le.assumption.
 qed.
 
+(* ??? this needs not le *)
+theorem S_pred: \forall n:nat.lt O n \to eq nat n (S (pred n)).
+intro.elim n.apply False_ind.exact not_le_Sn_O O H.
+apply eq_f.apply pred_Sn.
+qed.
+
 (* le vs. lt *)
 theorem lt_to_le : \forall n,m:nat. lt n m \to le n m.
 simplify.intros.elim H.
@@ -150,6 +156,4 @@ intros.simplify.right.exact not_le_Sn_O n1.
 intros 2.simplify.intro.elim H.
 left.apply le_S_S.assumption.
 right.intro.apply H1.apply le_S_S_to_le.assumption.
-qed.
-
-
+qed.
\ No newline at end of file