proof by "introduction" (impi) implemented in full

[helm.git] / matita / contribs / LOGIC / Track / order.ma

diff --git a/matita/contribs/LOGIC/Track/order.ma b/matita/contribs/LOGIC/Track/order.ma
index ee813d62cc744b71cd54c3152deec562650e8f0c..de6ebaf719c0c3ca9b1eaad9dc1b755b26624b76 100644 (file)
--- a/matita/contribs/LOGIC/Track/order.ma
+++ b/matita/contribs/LOGIC/Track/order.ma
@@ -20,76 +20,84 @@ include "Track/props.ma".
 
 theorem track_refl: \forall P. \forall c:Formula. \exists r. 
                     Track P r (pair c c).
- intros. elim c; clear c;
+ intros; elim c; clear c;
  [ autobatch
  | lapply (insert_total (pair f f1) zero P); [2:autobatch];
-   decompose. autobatch depth = 5 
+   decompose; autobatch depth = 5 width = 4 size = 8
  ].
 qed.
-
+(*
 theorem track_trans: \forall p,q,A,B. \forall c:Formula.
                      Track leaf p (pair A c) \to Track leaf q (pair c B) \to
                      \exists r. Track leaf r (pair A B).
  intros 1; elim p names 0; clear p;
- [ intros. clear H1.
-   lapply linear track_inv_lref to H. decompose.
-   lapply insert_inv_leaf_2 to H. decompose
- | intros.
-   lapply linear track_inv_parx to H. subst. autobatch.
- | intros.
-   lapply linear track_inv_impw to H1.
-   decompose. subst.
-   lapply linear H to H4, H2. decompose. autobatch
- | intros 3. elim q; clear q;
-   [ clear H H1.
-     lapply linear track_inv_lref to H2. decompose.
-     lapply insert_inv_leaf_2 to H. decompose
-   | lapply linear track_inv_parx to H2. subst. autobatch
-   | clear H H1.
-     lapply linear track_inv_impi to H2.
-     lapply linear track_inv_impw to H3.
-     decompose. subst. autobatch
-   | clear H H1 H2.
-     lapply linear track_inv_impi to H3.
-     decompose. subst
-   | clear H H1.
-     lapply linear track_inv_impi to H2.
-     lapply linear track_inv_impe to H3.
-     decompose. subst. autobatch
+ [ intros; clear H1;
+   lapply linear track_inv_lref to H; decompose;
+   lapply insert_inv_leaf_2 to H; decompose
+ | intros;
+   lapply linear track_inv_parx to H; subst; autobatch;
+ | intros;
+   lapply linear track_inv_impw to H1;
+   decompose; subst;
+   lapply linear H to H4, H2; decompose; autobatch
+ | intros 3; elim q; clear q;
+   [ clear H H1;
+     lapply linear track_inv_lref to H2; decompose;
+     lapply insert_inv_leaf_2 to H; decompose
+   | lapply linear track_inv_parx to H2; subst; autobatch
+   | clear H H1;
+     lapply linear track_inv_impr to H2;
+     lapply linear track_inv_impw to H3;
+     decompose; subst; autobatch
+   | clear H H1 H2;
+     lapply linear track_inv_impr to H3;
+     decompose; subst
+   | clear H2 H3;
+     lapply linear track_inv_impr to H4;
+     lapply linear track_inv_impi to H5;
+     decompose; subst;
+     lapply linear H to H5, H8; decompose;
+     
+     
+     lapply linear insert_inv_leaf_1 to H4; decompose; subst;
+     apply ex_intro; [| ]
+     
+     autobatch depth = 100 width = 40 size = 100
    ]
- | intros 3. elim q; clear q;
-   [ clear H H1.
-     lapply linear track_inv_lref to H2. decompose.
-     lapply insert_inv_leaf_2 to H. decompose 
-   | clear H.
-     lapply linear track_inv_parx to H2.
-     subst. autobatch
-   | clear H H1.
-     lapply linear track_inv_impe to H2.
-     lapply linear track_inv_impw to H3.
-     decompose. subst. autobatch
-   | clear H H1 H2.
-     lapply linear track_inv_impi to H3. decompose. subst
-   | clear H H1.
-     lapply linear track_inv_impe to H2.
-     lapply linear track_inv_impe to H3.
-     decompose. subst.
-     lapply linear track_inv_lleaf_impl to H5. decompose; subst;
-     [ clear H4 H6.
-       lapply linear insert_inv_leaf_1 to H3. decompose. subst.
-       lapply linear insert_inv_abst_2 to H2. decompose. subst
-     | lapply insert_conf to H3, H4. clear H4. decompose.
-       lapply linear track_weak to H6, H4. decompose.
-       lapply linear track_comp to H2, H, H1. decompose. autobatch
+ | intros 3; elim q; clear q;
+   [ clear H H1;
+     lapply linear track_inv_lref to H2; decompose;
+     lapply insert_inv_leaf_2 to H; decompose 
+   | clear H;
+     lapply linear track_inv_parx to H2;
+     subst; autobatch
+   | clear H H1;
+     lapply linear track_inv_impe to H2;
+     lapply linear track_inv_impw to H3;
+     decompose; subst; autobatch
+   | clear H H1 H2;
+     lapply linear track_inv_impi to H3; decompose; subst
+   | clear H H1;
+     lapply linear track_inv_impe to H2;
+     lapply linear track_inv_impe to H3;
+     decompose; subst;
+     lapply linear track_inv_lleaf_impl to H5; decompose; subst;
+     [ clear H4 H6;
+       lapply linear insert_inv_leaf_1 to H3; decompose; subst;
+       lapply linear insert_inv_abst_2 to H2; decompose; subst
+     | lapply insert_conf to H3, H4; clear H4; decompose;
+       lapply linear track_weak to H6, H4; decompose;
+       lapply linear track_comp to H2, H, H1; decompose; autobatch
      ]
    ]
  ].
 qed.    
 (*   
-   | lapply linear track_inv_impi to H4.
-     lapply linear track_inv_impe to H5.
-     decompose. subst.
-     destruct H4. destruct H5. clear H4 H5. subst.
-     unfold linj in Hcut. unfold rinj in Hcut3. destruct Hcut. destruct Hcut3. clear Hcut Hcut3. subst.
-     destruct Hcut2. clear Hcut2. subst.
+   | lapply linear track_inv_impi to H4;
+     lapply linear track_inv_impe to H5;
+     decompose; subst;
+     destruct H4; destruct H5; clear H4 H5; subst;
+     unfold linj in Hcut; unfold rinj in Hcut3; destruct Hcut; destruct Hcut3; clear Hcut Hcut3; subst;
+     destruct Hcut2; clear Hcut2; subst;
+*)
 *)