From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Wed, 2 May 2007 09:53:20 +0000 (+0000)
Subject: some improvements
X-Git-Tag: 0.4.95@7852~490
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=e167bc0b0d1e770cdd5994ade002335b88f87b65;p=helm.git

some improvements
---

diff --git a/matita/contribs/RELATIONAL/NPlus/monoid.ma b/matita/contribs/RELATIONAL/NPlus/monoid.ma
index 4d1705b90..368396a77 100644
--- a/matita/contribs/RELATIONAL/NPlus/monoid.ma
+++ b/matita/contribs/RELATIONAL/NPlus/monoid.ma
@@ -39,6 +39,19 @@ theorem nplus_comm_rew: \forall p,q,r. (p + q == r) \to q + p == r.
  intros. elim H; clear H q r; auto.
 qed.
 
+theorem nplus_ass: \forall p1, p2, r1. (p1 + p2 == r1) \to
+                   \forall p3, s1. (r1 + p3 == s1) \to
+                   \forall r3. (p2 + p3 == r3) \to 
+                   \forall s3. (p1 + r3 == s3) \to s1 = s3.
+ intros 4. elim H; clear H p2 r1;
+ [ lapply linear nplus_inv_zero_1 to H2. subst.
+   lapply nplus_mono to H1, H3. subst. auto
+ | lapply linear nplus_inv_succ_1 to H3. decompose. subst.
+   lapply linear nplus_inv_succ_1 to H4. decompose. subst.
+   lapply linear nplus_inv_succ_2 to H5. decompose. subst. auto
+ ].
+qed.
+ 
 (* Corollaries of functional properties **************************************)
 
 theorem nplus_inj_2: \forall p, q1, r. (p + q1 == r) \to