proof by "introduction" (impi) implemented in full

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

diff --git a/matita/contribs/LOGIC/Track/props.ma b/matita/contribs/LOGIC/Track/props.ma
index a7d79f57199b35bfeddb9b0e5bdcdcff62d0e954..fc57cf0062ae08cf0f9e1765d874a1c58d2e3340 100644 (file)
--- a/matita/contribs/LOGIC/Track/props.ma
+++ b/matita/contribs/LOGIC/Track/props.ma
@@ -20,34 +20,38 @@ include "Track/inv.ma".
 theorem track_weak: \forall R,p,P,Q,S,i. 
                     Track P p S \to Insert R i P Q \to 
                     \exists q. Track Q q S.
- intros 2. elim p; clear p;
+ intros 2; elim p; clear p;
  [ lapply linear track_inv_lref to H as H0; decompose;
    lapply linear insert_trans to H, H1; decompose; autobatch
- | lapply linear track_inv_parx to H. subst. autobatch
- | lapply linear track_inv_impw to H1. decompose. subst.
-   lapply linear H to H4, H2. decompose. autobatch
- | lapply linear track_inv_impi to H1. decompose. subst.
-   lapply linear H to H4, H2. decompose. autobatch
- | lapply linear track_inv_impe to H1. decompose. subst.
-   lapply linear insert_conf to H2, H4. decompose.
-   lapply linear H to H5, H3. decompose. autobatch
+ | lapply linear track_inv_parx to H; subst; autobatch
+ | lapply linear track_inv_impw to H1; decompose; subst;
+   lapply linear H to H4, H2; decompose; autobatch
+ | lapply linear track_inv_impr to H1; decompose; subst;
+   lapply linear H to H4, H2; decompose; autobatch
+ | lapply linear track_inv_impi to H3; decompose; subst;
+   lapply insert_conf to H4, H6; clear H6; decompose;
+   lapply H to H9, H4; clear H H9; lapply linear H1 to H8, H4;
+   lapply linear H2 to H7, H6; decompose; autobatch width = 4
+ | lapply linear track_inv_scut to H2; decompose
  ]
 qed.
 
 theorem track_comp: \forall R,q,p,P,Q,S,i. 
                     Track P p R \to Track Q q S \to Insert R i P Q \to
                     \exists r. Track P r S.
- intros 2. elim q; clear q;
+ intros 2; elim q; clear q;
  [ lapply linear track_inv_lref to H1 as H0; decompose;
    lapply linear insert_conf_rev_full to H1,H2; decompose; subst; autobatch
- | lapply linear track_inv_parx to H1. subst. autobatch
- | lapply linear track_inv_impw to H2. decompose. subst.
-   lapply linear H to H1, H5, H3. decompose. autobatch
- | lapply linear track_inv_impi to H2. decompose. subst.
-   lapply linear H to H1, H5, H3. decompose. autobatch
- | lapply linear track_inv_impe to H2. decompose. subst.
-   lapply linear insert_trans to H3, H5. decompose.
-   lapply track_weak to H1, H3. clear H1. decompose.
-   lapply linear H to H1, H6, H4. decompose. autobatch
+ | lapply linear track_inv_parx to H1; subst; autobatch
+ | lapply linear track_inv_impw to H2; decompose; subst;
+   lapply linear H to H1, H5, H3; decompose; autobatch
+ | lapply linear track_inv_impr to H2; decompose; subst;
+   lapply linear H to H1, H5, H3; decompose; autobatch
+ | lapply linear track_inv_impi to H4; decompose; subst;
+   lapply insert_trans to H5, H7; clear H7; decompose;
+   lapply track_weak to H3, H6; decompose;
+   lapply H to H3, H10, H5; clear H H10; lapply linear H1 to H3, H9, H5;
+   lapply linear H2 to H4, H8, H7; decompose; autobatch width = 4
+ | lapply linear track_inv_scut to H3; decompose
  ].
 qed.