some corrections ...

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / lib / arith.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
index 832195fe90efcf4e404c39af1e6ed4f37eabd5ac..92b07e1f2b9525a4bbd743f498ede54a2860e057 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
@@ -52,12 +52,21 @@ lemma arith_i: ∀x,y,z. y < x → x+z-y-1 = x-y-1+z.
 
 (* Properties ***************************************************************)
 
-fact le_repl_sn_aux: ∀x,y,z:nat. x ≤ z → x = y → y ≤ z.
+fact le_repl_sn_conf_aux: ∀x,y,z:nat. x ≤ z → x = y → y ≤ z.
+// qed-.
+
+fact le_repl_sn_trans_aux: ∀x,y,z:nat. x ≤ z → y = x → y ≤ z.
 // qed-.
 
 lemma monotonic_le_minus_l2: ∀x1,x2,y,z. x1 ≤ x2 → x1 - y - z ≤ x2 - y - z.
 /3 width=1 by monotonic_le_minus_l/ qed.
 
+(* Note: this might interfere with nat.ma *)
+lemma monotonic_lt_pred: ∀m,n. m < n → O < m → pred m < pred n.
+#m #n #Hmn #Hm whd >(S_pred … Hm)
+@le_S_S_to_le >S_pred /2 width=3 by transitive_lt/
+qed.
+
 lemma arith_j: ∀x,y,z. x-y-1 ≤ x-(y-z)-1.
 /3 width=1 by monotonic_le_minus_l, monotonic_le_minus_r/ qed.