X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FRELATIONAL%2FNPlus%2Fmonoid.ma;h=1ccd6417e4d117eb47e14be0c02b2e292638be2a;hb=5e736134ceab076b4e963d535f380ffa796a5d19;hp=4d1705b90da0d1eba00f5e98cd5958c2fc639344;hpb=93cc04b6bdb9772d8e4d96cf019ad8394e26b92a;p=helm.git

diff --git a/helm/software/matita/contribs/RELATIONAL/NPlus/monoid.ma b/helm/software/matita/contribs/RELATIONAL/NPlus/monoid.ma
index 4d1705b90..1ccd6417e 100644
--- a/helm/software/matita/contribs/RELATIONAL/NPlus/monoid.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NPlus/monoid.ma
@@ -19,12 +19,12 @@ include "NPlus/fun.ma".
 (* Monoidal properties ******************************************************)
 
 theorem nplus_zero_1: \forall q. zero + q == q.
- intros. elim q; clear q; auto.
+ intros. elim q; clear q; autobatch.
 qed.
 
 theorem nplus_succ_1: \forall p,q,r. (p + q == r) \to 
                       (succ p) + q == (succ r).
- intros. elim H; clear H q r; auto.
+ intros. elim H; clear H q r; autobatch.
 qed.
 
 theorem nplus_comm: \forall p, q, x. (p + q == x) \to
@@ -32,18 +32,31 @@ theorem nplus_comm: \forall p, q, x. (p + q == x) \to
  intros 4; elim H; clear H q x;
  [ lapply linear nplus_inv_zero_1 to H1
  | lapply linear nplus_inv_succ_1 to H3. decompose
- ]; subst; auto.
+ ]; subst; autobatch.
 qed.
 
 theorem nplus_comm_rew: \forall p,q,r. (p + q == r) \to q + p == r.
- intros. elim H; clear H q r; auto.
+ intros. elim H; clear H q r; autobatch.
 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. autobatch
+ | 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. autobatch
+ ].
+qed.
+ 
 (* Corollaries of functional properties **************************************)
 
 theorem nplus_inj_2: \forall p, q1, r. (p + q1 == r) \to
                      \forall q2. (p + q2 == r) \to q1 = q2.
- intros. auto.
+ intros. autobatch.
 qed.
 
 (* Corollaries of nonoidal properties ***************************************)
@@ -58,7 +71,7 @@ theorem nplus_comm_1: \forall p1, q, r1. (p1 + q == r1) \to
  | lapply linear nplus_inv_succ_2 to H3.
    lapply linear nplus_inv_succ_2 to H4. decompose. subst.
    lapply linear nplus_inv_succ_2 to H5. decompose
- ]; subst; auto.
+ ]; subst; autobatch.
 qed.
 
 theorem nplus_comm_1_rew: \forall p1,q,r1. (p1 + q == r1) \to
@@ -68,7 +81,7 @@ theorem nplus_comm_1_rew: \forall p1,q,r1. (p1 + q == r1) \to
  [ lapply linear nplus_inv_zero_2 to H1. subst
  | lapply linear nplus_inv_succ_2 to H3. decompose. subst.
    lapply linear nplus_inv_succ_2 to H4. decompose. subst
- ]; auto.
+ ]; autobatch.
 qed.
 
 (*