X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Flib%2Farith.ma;h=dcf7e2de0d3d303ea1c4f1289f6f0be445182511;hb=dffdece065d12d9961a6c3f1222f6d112030336f;hp=3eec591c692269b16eae8bff92bb6efbfb7bc4cf;hpb=87fbbf33fcc2ed91cc8b8a08e1c378ef49ac723d;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
index 3eec591c6..dcf7e2de0 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
@@ -19,6 +19,14 @@ include "ground_2/lib/star.ma".
 
 (* Equations ****************************************************************)
 
+(* Note: uses minus_minus_comm, minus_plus_m_m, commutative_plus, plus_minus *)
+lemma plus_minus_minus_be: ∀x,y,z. y ≤ z → z ≤ x → (x - z) + (z - y) = x - y.
+#x #z #y #Hzy #Hyx >plus_minus // >commutative_plus >plus_minus //
+qed-.
+
+fact plus_minus_minus_be_aux: ∀i,x,y,z. y ≤ z → z ≤ x → i = z - y → x - z + i = x - y.
+/2 width=1 by plus_minus_minus_be/ qed-.
+
 lemma plus_n_2: ∀n. n + 2 = n + 1 + 1.
 // qed.