unified: some theorems on Lift started

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

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/fwd.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/fwd.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/fwd".
+
+include "Lift/defs.ma".
+
+theorem lift_sort_1: \forall q, h, d, k, x.
+                     Lift q h d (leaf (sort k)) x \to
+                     x = leaf (sort k).
+ intros. inversion H; clear H; intros;
+ [ auto
+ | destruct H3
+ | destruct H4
+ | destruct H5
+ | destruct H7
+ | destruct H7
+ | destruct H8
+ ].
+qed.
+
+theorem lift_lref_1: \forall q, h, d, k, x.
+                     Lift q h d (leaf (lref k)) x \to
+                     (q = false \land x = leaf (lref k)) \lor
+                     (q = true \land k < d \land x = leaf (lref k)) \lor
+                     (q = true \land d <= k \land 
+                     \exists e. (k + h == e) \land x = leaf (lref e)
+                    ). 
+ intros. inversion H; clear H; intros;
+ [ destruct H3
+ | destruct H3. clear H3. subst. auto depth = 4
+ | destruct H4. clear H4. subst. auto depth = 5
+ | destruct H5. clear H5. subst. auto depth = 5
+ | destruct H7
+ | destruct H7
+ | destruct H8
+ ].
+qed.
+
+theorem lift_head_1: \forall q, l, i, p, z, u1, t1, x.
+                     Lift q l i (head p z u1 t1) x \to
+                     (p = q \land
+                                 \exists r, u2, t2. 
+                                 z = bind r \land
+                                 Lift true l i u1 u2 \land Lift q l (succ i) t1 t2 \land
+                                 x = head p z u2 t2
+                                ) \lor
+                                (p = q \land 
+                                 \exists r,u2,t2. 
+                                 z = flat r \land
+                                 Lift true l i u1 u2 \land Lift q l i t1 t2 \land
+                                 x = head p z u2 t2
+                                ) \lor
+                                ((p = q \to False) \land
+                                 \exists u2,t2.
+                                 Lift true l i u1 u2 \land Lift q l i t1 t2 \land
+                                 x = head p z u2 t2
+                                ).
+ intros. inversion H; clear H; intros;
+ [ destruct H3
+ | destruct H3
+ | destruct H4
+ | destruct H5
+ | destruct H7. clear H7 H1 H3. subst. auto depth = 10
+ | destruct H7. clear H7 H1 H3. subst. auto depth = 10
+ | destruct H8. clear H8 H2 H4. subst. auto depth = 7
+ ].
+qed.
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