contribs: some improvements

[helm.git] / helm / software / matita / contribs / LAMBDA-TYPES / Unified-Sub / Lift / inv.ma

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
new file mode 100644 (file)
index 0000000..8c3d27d
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/inv.ma
@@ -0,0 +1,74 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/Unified-Sub/Lift/inv".
+
+include "Lift/defs.ma".
+
+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
+ ].
+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
+                         (i <= j1 \land 
+                          \exists j2. (l + j1 == j2) \land x = leaf (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
+ ].
+qed.
+
+theorem lift_inv_bind_1: \forall l, i, r, u1, t1, x.
+                         Lift l i (intb r u1 t1) x \to
+                         \exists u2, t2. 
+                         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
+ ].
+qed.
+
+theorem lift_inv_flat_1: \forall l, i, r, u1, t1, x.
+                         Lift l i (intf r u1 t1) x \to
+                         \exists u2, t2. 
+                         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
+ ].
+qed.