X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fground_2%2Farith.ma;h=ad3ab4a3d5dab681e6971977d0d3e078251275ec;hb=315610badd512e271f6e99011721a3b4d3e316fc;hp=c51873baa09bb9d8f0c46e2f502e378cb05af921;hpb=b074ebf6441993694c6e39e4eaeeb58a3186f479;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/ground_2/arith.ma b/matita/matita/contribs/lambda_delta/ground_2/arith.ma
index c51873baa..ad3ab4a3d 100644
--- a/matita/matita/contribs/lambda_delta/ground_2/arith.ma
+++ b/matita/matita/contribs/lambda_delta/ground_2/arith.ma
@@ -69,6 +69,17 @@ lemma false_lt_to_le: ∀x,y. (x < y → ⊥) → y ≤ x.
 #Hxy elim (H Hxy)
 qed-.
 
+lemma le_plus_xySz_x_false: ∀y,z,x. x + y + S z ≤ x → ⊥.
+#y #z #x elim x -x
+[ #H lapply (le_n_O_to_eq … H) -H
+  <plus_n_Sm #H destruct
+| /3 width=1 by le_S_S_to_le/
+]
+qed-.
+
+lemma plus_xySz_x_false: ∀z,x,y. x + y + S z = x → ⊥.
+/2 width=4 by le_plus_xySz_x_false/ qed-.
+
 (* iterators ****************************************************************)
 
 (* Note: see also: lib/arithemetcs/bigops.ma *)