X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fcontribs%2FRELATIONAL%2FNPlus%2Fmonoid.ma;h=a521c9a1dfef29b49f0176f484f0bf4e9eac3383;hb=cf5540f056d6d4fa1612e08d41253d1d009f5d44;hp=1ccd6417e4d117eb47e14be0c02b2e292638be2a;hpb=72a05c70f5ab9dabb704f1dc334920b10a8f4bb9;p=helm.git

diff --git a/matita/contribs/RELATIONAL/NPlus/monoid.ma b/matita/contribs/RELATIONAL/NPlus/monoid.ma
index 1ccd6417e..a521c9a1d 100644
--- a/matita/contribs/RELATIONAL/NPlus/monoid.ma
+++ b/matita/contribs/RELATIONAL/NPlus/monoid.ma
@@ -32,7 +32,7 @@ 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; autobatch.
+ ]; destruct; autobatch.
 qed.
 
 theorem nplus_comm_rew: \forall p,q,r. (p + q == r) \to q + p == r.
@@ -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. 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
+ [ 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.
  
@@ -69,18 +69,18 @@ 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; autobatch.
+ ]; 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
+ [ 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 ]. (**)