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diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma
index f1824e22e..da1de97f5 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma
@@ -15,9 +15,9 @@
 include "ground/arith/nat_pred_succ.ma".
 include "ground/arith/nat_le.ma".
 
-(* NON-NEGATIVE INTEGERS ****************************************************)
+(* ORDER FOR NON-NEGATIVE INTEGERS ******************************************)
 
-(* Basic constructions with pred ********************************************)
+(* Constructions with npred *************************************************)
 
 (*** le_pred_n *)
 lemma nle_pred_sn_refl (m): ↓m ≤ m.
@@ -26,6 +26,18 @@ qed.
 
 (*** monotonic_pred *)
 lemma nle_pred_bi (m) (n): m ≤ n → ↓m ≤ ↓n.
-#m #n #H elim H -n
+#m #n #H elim H -n //
 /2 width=3 by nle_trans/
 qed.
+
+lemma nle_pred_sn (m) (n): m ≤ ↑n → ↓m ≤ n.
+#m #n elim m -m //
+/2 width=1 by nle_pred_bi/
+qed-.
+
+(* Destructions with npred **************************************************)
+
+lemma nle_inv_pred_sn (m) (n): ↓m ≤ n → m ≤ ↑n.
+#m #n elim m -m
+/2 width=1 by nle_succ_bi/
+qed-.