arithmetics for λδ

[helm.git] / matita / matita / contribs / lambdadelta / ground / arith / nat_le_pred.ma

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 75cd4bf7e676a5030b79111112c3cc43501af595..0454acee027d23a65ce36344164c974d7425a339 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma
@@ -20,7 +20,7 @@ include "ground/arith/nat_le.ma".
 (* Destructions with npred **************************************************)
 
 lemma nle_inv_pred_sn (m) (n): ↓m ≤ n → m ≤ ↑n.
-#m #n elim m -m
+#m #n @(nat_ind_succ … m) -m
 /2 width=1 by nle_succ_bi/
 qed-.
 
@@ -31,7 +31,7 @@ lemma nle_succ_pred_dx_refl (m): m ≤ ↑↓m.
 
 (*** le_pred_n *)
 lemma nle_pred_sn_refl (m): ↓m ≤ m.
-#m elim m -m //
+#m @(nat_ind_succ … m) -m //
 qed.
 
 (*** monotonic_pred *)
@@ -41,6 +41,6 @@ lemma nle_pred_bi (m) (n): m ≤ n → ↓m ≤ ↓n.
 qed.
 
 lemma nle_pred_sn (m) (n): m ≤ ↑n → ↓m ≤ n.
-#m #n elim m -m //
+#m #n @(nat_ind_succ … m) -m //
 /2 width=1 by nle_pred_bi/
 qed-.