X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FRELATIONAL%2FNPlus%2Fmonoid.ma;h=7fc7988780c1602ed606c7ed159f365070abec56;hb=bf8fe5331d6e6d2dfe955efa54b1ffdafaae8429;hp=368396a778e5afa5cf55634560b56ffdc80a7266;hpb=effab341df3fb2bfe403e51d360e81c8b0455e1a;p=helm.git

diff --git a/helm/software/matita/contribs/RELATIONAL/NPlus/monoid.ma b/helm/software/matita/contribs/RELATIONAL/NPlus/monoid.ma
index 368396a77..7fc798878 100644
--- a/helm/software/matita/contribs/RELATIONAL/NPlus/monoid.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NPlus/monoid.ma
@@ -12,19 +12,19 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/RELATIONAL/NPlus/monoid".
+
 
 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
@@ -32,11 +32,11 @@ 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.
+ ]; destruct; 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
@@ -44,11 +44,11 @@ theorem nplus_ass: \forall p1, p2, r1. (p1 + p2 == r1) \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
+ [ lapply linear nplus_inv_zero_1 to H2. destruct.
+   lapply nplus_mono to H1, H3. destruct. autobatch
+ | lapply linear nplus_inv_succ_1 to H3. decompose. destruct.
+   lapply linear nplus_inv_succ_1 to H4. decompose. destruct.
+   lapply linear nplus_inv_succ_2 to H5. decompose. destruct. autobatch
  ].
 qed.
  
@@ -56,7 +56,7 @@ qed.
 
 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 ***************************************)
@@ -69,19 +69,19 @@ theorem nplus_comm_1: \forall p1, q, r1. (p1 + q == r1) \to
  intros 4. elim H; clear H q r1;
  [ lapply linear nplus_inv_zero_2 to H1
  | 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 H4. decompose. destruct.
    lapply linear nplus_inv_succ_2 to H5. decompose
- ]; subst; auto.
+ ]; destruct; autobatch.
 qed.
 
 theorem nplus_comm_1_rew: \forall p1,q,r1. (p1 + q == r1) \to
                           \forall p2,r2. (p2 + q == r2) \to
                           \forall s. (p1 + r2 == s) \to (p2 + r1 == s).
  intros 4. elim H; clear H q r1;
- [ 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.
+ [ lapply linear nplus_inv_zero_2 to H1. destruct
+ | lapply linear nplus_inv_succ_2 to H3. decompose. destruct.
+   lapply linear nplus_inv_succ_2 to H4. decompose. destruct
+ ]; autobatch.
 qed.
 
 (*                      
@@ -89,14 +89,14 @@ theorem nplus_shift_succ_sx: \forall p,q,r.
                              (p + (succ q) == r) \to (succ p) + q == r.
  intros.
  lapply linear nplus_inv_succ_2 to H as H0.
- decompose. subst. auto new timeout=100.
+ decompose. destruct. auto new timeout=100.
 qed.
 
 theorem nplus_shift_succ_dx: \forall p,q,r. 
                              ((succ p) + q == r) \to p + (succ q) == r.
  intros.
  lapply linear nplus_inv_succ_1 to H as H0.
- decompose. subst. auto new timeout=100.
+ decompose. destruct. auto new timeout=100.
 qed.
 
 theorem nplus_trans_1: \forall p,q1,r1. (p + q1 == r1) \to 
@@ -104,11 +104,11 @@ theorem nplus_trans_1: \forall p,q1,r1. (p + q1 == r1) \to
                        \exists q. (q1 + q2 == q) \land p + q == r2.
  intros 2; elim q1; clear q1; intros;
  [ lapply linear nplus_inv_zero_2 to H as H0.
-   subst.
+   destruct.
  | lapply linear nplus_inv_succ_2 to H1 as H0.
-   decompose. subst.
+   decompose. destruct.
    lapply linear nplus_inv_succ_1 to H2 as H0.
-   decompose. subst.
+   decompose. destruct.
    lapply linear H to H4, H3 as H0.
    decompose.
  ]; apply ex_intro; [| auto new timeout=100 || auto new timeout=100 ]. (**)
@@ -119,11 +119,11 @@ theorem nplus_trans_2: \forall p1,q,r1. (p1 + q == r1) \to
                        \exists p. (p1 + p2 == p) \land p + q == r2.
  intros 2; elim q; clear q; intros;
  [ lapply linear nplus_inv_zero_2 to H as H0.
-   subst
+   destruct
  | lapply linear nplus_inv_succ_2 to H1 as H0.
-   decompose. subst.
+   decompose. destruct.
    lapply linear nplus_inv_succ_2 to H2 as H0.
-   decompose. subst.
+   decompose. destruct.
    lapply linear H to H4, H3 as H0.
    decompose.
  ]; apply ex_intro; [| auto new timeout=100 || auto new timeout=100 ]. (**)