X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_le_minus.ma;h=5656acffd1c61acc1eb9a4618f91a057f12d8370;hb=21de0d35017656c5a55528390b54b0b2ae395b44;hp=e3da0c92262e6682a676a87f120711c8be8169db;hpb=5e72e41f4f86814e56d4b00959ccc56c71042a4c;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_le_minus.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_le_minus.ma
index e3da0c922..5656acffd 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_le_minus.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_le_minus.ma
@@ -21,19 +21,22 @@ include "ground/arith/nat_le_pred.ma".
 
 (*** minus_le *)
 lemma nle_minus_sn_refl_sn (m) (n): m - n ≤ m.
-#m #n elim n -n //
+#m #n @(nat_ind_succ … n) -n //
 #n #IH /2 width=3 by nle_trans/
 qed.
 
+lemma nle_minus_succ_sn (m) (n): ↑n - m ≤ ↑(n - m).
+// qed.
+
 (*** inv_eq_minus_O *)
 lemma nle_eq_minus_O (m) (n): 𝟎 = m - n → m ≤ n.
-#m #n @(nat_ind_2 … m n) //
+#m #n @(nat_ind_succ_2 … m n) //
 /3 width=1 by nle_succ_bi/
 qed.
 
 (*** monotonic_le_minus_l *)
 lemma nle_minus_sn_bi (m) (n) (o): m ≤ n → m-o ≤ n-o.
-#m #n #o elim o -o //
+#m #n #o @(nat_ind_succ … o) -o //
 #o #IH #Hmn /3 width=1 by nle_pred_bi/
 qed.