X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Flib%2Farith.ma;h=24d1d47fbd4005dc5848c0321098af78766f7f5b;hb=d71e53021b0c17e1a00c2d623e7139c6d18069d5;hp=e3ec5c5040847cd64f141efd9aede61dcee4f658;hpb=1083ac3b1acac5f1ac1fa40a9a417dd9d268dced;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 e3ec5c504..24d1d47fb 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
@@ -60,10 +60,6 @@ lemma minus_plus_m_m_commutative: ∀n,m:nat. n = m + n - m.
 lemma plus_n_2: ∀n. n + 2 = n + 1 + 1.
 // qed.
 
-lemma arith_l: ∀x. 1 = 1-x+(x-(x-1)).
-* // #x >minus_S_S >minus_S_S <minus_O_n <minus_n_O //
-qed.
-
 (* 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 //
@@ -150,6 +146,13 @@ lemma monotonic_le_minus_l2: ∀x1,x2,y,z. x1 ≤ x2 → x1 - y - z ≤ x2 - y -
 lemma minus_le_trans_sn: ∀x1,x2. x1 ≤ x2 → ∀x. x1-x ≤ x2.
 /2 width=3 by transitive_le/ qed.
 
+lemma le_plus_to_minus_l: ∀a,b,c. a + b ≤ c → b ≤ c-a.
+/2 width=1 by le_plus_to_minus_r/
+qed-.
+
+lemma le_plus_to_minus_comm: ∀n,m,p. n ≤ p+m → n-p ≤ m.
+/2 width=1 by le_plus_to_minus/ qed-.
+
 (* Note: this might interfere with nat.ma *)
 lemma monotonic_lt_pred: ∀m,n. m < n → 0 < m → pred m < pred n.
 #m #n #Hmn #Hm whd >(S_pred … Hm)