X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FUnified-Sub%2FLift%2Finv.ma;h=bbd8d744e7238a0d6ffd8e532080cf5bd50ae34c;hb=5c1b44dfefa085fbb56e23047652d3650be9d855;hp=d664e5f0724dee1dc62e59b78ae33d71185b827f;hpb=2b95f946837707c6ad30d1b8317d73c55cda3dc8;p=helm.git

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/inv.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/inv.ma
index d664e5f07..bbd8d744e 100644
--- a/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/inv.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/inv.ma
@@ -12,37 +12,25 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/LAMBDA-TYPES/Unified-Sub/Lift/inv".
+
 
 include "Lift/defs.ma".
 
 (* Inversion properties *****************************************************)
 
 theorem lift_inv_sort_1: \forall l, i, h, x.
-                         Lift l i (leaf (sort h)) x \to
-                         x = leaf (sort h).
- intros. inversion H; clear H; intros;
- [ auto
- | destruct H2
- | destruct H3
- | destruct H5
- | destruct H5
- ].
+                         Lift l i (sort h) x \to
+                         x = sort h.
+ intros. inversion H; clear H; intros; destruct. autobatch.
 qed.
 
 theorem lift_inv_lref_1: \forall l, i, j1, x.
-                         Lift l i (leaf (lref j1)) x \to
-                         (i > j1 \land x = leaf (lref j1)) \lor
+                         Lift l i (lref j1) x \to
+                         (i > j1 \land x = lref j1) \lor
                          (i <= j1 \land 
-                          \exists j2. (l + j1 == j2) \land x = leaf (lref j2)
+                          \exists j2. (l + j1 == j2) \land x = lref j2
                          ).
- intros. inversion H; clear H; intros;
- [ destruct H1
- | destruct H2. clear H2. subst. auto
- | destruct H3. clear H3. subst. auto depth = 5
- | destruct H5
- | destruct H5
- ].
+ intros. inversion H; clear H; intros; destruct; autobatch depth = 5 size = 7.
 qed.
 
 theorem lift_inv_bind_1: \forall l, i, r, u1, t1, x.
@@ -51,13 +39,7 @@ theorem lift_inv_bind_1: \forall l, i, r, u1, t1, x.
                          Lift l i u1 u2 \land
                          Lift l (succ i) t1 t2 \land
                          x = intb r u2 t2.
- intros. inversion H; clear H; intros;
- [ destruct H1
- | destruct H2
- | destruct H3
- | destruct H5. clear H5 H1 H3. subst. auto depth = 5
- | destruct H5
- ].
+ intros. inversion H; clear H; intros; destruct; autobatch depth = 5 size = 7.
 qed.
 
 theorem lift_inv_flat_1: \forall l, i, r, u1, t1, x.
@@ -66,40 +48,22 @@ theorem lift_inv_flat_1: \forall l, i, r, u1, t1, x.
                          Lift l i u1 u2 \land
                          Lift l i t1 t2 \land
                          x = intf r u2 t2.
- intros. inversion H; clear H; intros;
- [ destruct H1
- | destruct H2
- | destruct H3
- | destruct H5 
- | destruct H5. clear H5 H1 H3. subst. auto depth = 5
- ].
+ intros. inversion H; clear H; intros; destruct. autobatch depth = 5 size = 7.
 qed.
 
 theorem lift_inv_sort_2: \forall l, i, x, h.
-                         Lift l i x (leaf (sort h)) \to
-                         x = leaf (sort h).
- intros. inversion H; clear H; intros;
- [ auto
- | destruct H3
- | destruct H4
- | destruct H6
- | destruct H6
- ].
+                         Lift l i x (sort h) \to
+                         x = sort h.
+ intros. inversion H; clear H; intros; destruct. autobatch.
 qed.
 
 theorem lift_inv_lref_2: \forall l, i, x, j2.
-                         Lift l i x (leaf (lref j2)) \to
-                         (i > j2 \land x = leaf (lref j2)) \lor
+                         Lift l i x (lref j2) \to
+                         (i > j2 \land x = lref j2) \lor
                          (i <= j2 \land 
-                          \exists j1. (l + j1 == j2) \land x = leaf (lref j1)
+                          \exists j1. (l + j1 == j2) \land x = lref j1
                          ).
- intros. inversion H; clear H; intros;
- [ destruct H2
- | destruct H3. clear H3. subst. auto
- | destruct H4. clear H4. subst. auto depth = 5
- | destruct H6
- | destruct H6
- ].
+ intros. inversion H; clear H; intros; destruct; autobatch depth = 5 size = 10.
 qed.
 
 theorem lift_inv_bind_2: \forall l, i, r, x, u2, t2.
@@ -108,13 +72,7 @@ theorem lift_inv_bind_2: \forall l, i, r, x, u2, t2.
                          Lift l i u1 u2 \land
                          Lift l (succ i) t1 t2 \land
                          x = intb r u1 t1.
- intros. inversion H; clear H; intros;
- [ destruct H2
- | destruct H3
- | destruct H4
- | destruct H6. clear H5 H1 H3. subst. auto depth = 5
- | destruct H6
- ].
+ intros. inversion H; clear H; intros; destruct. autobatch depth = 5 size = 7.
 qed.
 
 theorem lift_inv_flat_2: \forall l, i, r, x, u2, t2.
@@ -123,55 +81,69 @@ theorem lift_inv_flat_2: \forall l, i, r, x, u2, t2.
                          Lift l i u1 u2 \land
                          Lift l i t1 t2 \land
                          x = intf r u1 t1.
- intros. inversion H; clear H; intros;
- [ destruct H2
- | destruct H3
- | destruct H4
- | destruct H6 
- | destruct H6. clear H6 H1 H3. subst. auto depth = 5
- ].
+ intros. inversion H; clear H; intros; destruct. autobatch depth = 5 size = 7.
 qed.
 
 (* Corollaries of inversion properties ***************************************)
 
 theorem lift_inv_lref_1_gt: \forall l, i, j1, x.
-                            Lift l i (leaf (lref j1)) x \to
-                            i > j1 \to x = leaf (lref j1).
- intros 5.
- lapply linear lift_inv_lref_1 to H. decompose; subst;
- [ auto
+                            Lift l i (lref j1) x \to
+                            i > j1 \to x = lref j1.
+ intros.
+ lapply linear lift_inv_lref_1 to H. decompose; destruct;
+ [ autobatch
  | lapply linear nle_false to H2, H1. decompose
  ].
- qed.
+qed.
 
 theorem lift_inv_lref_1_le: \forall l, i, j1, x.
-                            Lift l i (leaf (lref j1)) x \to
-                            i <= j1 \to \forall j2. (l + j1 == j2) \to
-                            x = leaf (lref j2).
- intros 5.
- lapply linear lift_inv_lref_1 to H. decompose; subst;
+                            Lift l i (lref j1) x \to i <= j1 \to 
+                            \exists j2. (l + j1 == j2) \land x = lref j2.
+ intros.
+ lapply linear lift_inv_lref_1 to H. decompose; destruct;
+ [ lapply linear nle_false to H1, H2. decompose
+ | autobatch
+ ].
+qed.
+
+theorem lift_inv_lref_1_le_nplus: \forall l, i, j1, x.
+                                 Lift l i (lref j1) x \to
+                                 i <= j1 \to \forall j2. (l + j1 == j2) \to
+                                 x = lref j2.
+ intros.
+ lapply linear lift_inv_lref_1 to H. decompose; destruct;
  [ lapply linear nle_false to H1, H3. decompose
- | lapply linear nplus_mono to H2, H4. subst. auto
+ | lapply linear nplus_mono to H2, H4. destruct. autobatch
  ].
 qed.
 
 theorem lift_inv_lref_2_gt: \forall l, i, x, j2.
-                            Lift l i x (leaf (lref j2)) \to
-                            i > j2 \to x = leaf (lref j2).
- intros 5.
- lapply linear lift_inv_lref_2 to H. decompose; subst;
- [ auto
+                            Lift l i x (lref j2) \to
+                            i > j2 \to x = lref j2.
+ intros.
+ lapply linear lift_inv_lref_2 to H. decompose; destruct;
+ [ autobatch
  | lapply linear nle_false to H2, H1. decompose
  ].
  qed.
 
 theorem lift_inv_lref_2_le: \forall l, i, x, j2.
-                            Lift l i x (leaf (lref j2)) \to
-                            i <= j2 \to \forall j1. (l + j1 == j2) \to
-                            x = leaf (lref j1).
- intros 5.
- lapply linear lift_inv_lref_2 to H. decompose; subst;
+                            Lift l i x (lref j2) \to i <= j2 \to 
+                            \exists j1. (l + j1 == j2) \land x = lref j1.
+ intros.
+ lapply linear lift_inv_lref_2 to H. decompose; destruct;
+ [ lapply linear nle_false to H1, H2. decompose
+ | autobatch
+ ].
+qed.
+
+theorem lift_inv_lref_2_le_nplus: \forall l, i, x, j2.
+                                  Lift l i x (lref j2) \to
+                                  i <= j2 \to \forall j1. (l + j1 == j2) \to
+                                  x = lref j1.
+ intros.
+ lapply linear lift_inv_lref_2 to H. decompose; destruct;
  [ lapply linear nle_false to H1, H3. decompose
- | lapply linear nplus_inj_2 to H2, H4. subst. auto
+ | lapply linear nplus_inj_2 to H2, H4. destruct. autobatch
  ].
 qed.