unified: some theorems on Lift started

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/defs.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/defs.ma
index af573d3604f64e685edf1de289d02f756ebcb639..eac00ae357c40fcba2723dd85f1b7e3067c7c325 100644 (file)
--- a/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/defs.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/defs.ma
@@ -38,9 +38,9 @@ inductive Lift: Bool \to Nat \to Nat \to Term \to Term \to Prop \def
                    \forall q,t1,t2. Lift q l i t1 t2 \to 
                    \forall r.
                    Lift q l i (head q (flat r) u1 t1) (head q (flat r) u2 t2)
-   | lift_head   : \forall l,qt,q. (qt = q \to False) \to
+   | lift_head   : \forall l,q,p. (p = q \to False) \to
                    \forall i,u1,u2. Lift false l i u1 u2 \to
-                   \forall t1,t2. Lift qt l i t1 t2 \to 
+                   \forall t1,t2. Lift q l i t1 t2 \to 
                    \forall z.
-                   Lift qt l i (head q z u1 t1) (head q z u2 t2)
+                   Lift q l i (head p z u1 t1) (head p z u2 t2)
 .

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
new file mode 100644 (file)
index 0000000..9caab5d
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/fwd.ma
@@ -0,0 +1,79 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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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diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/props.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/props.ma
new file mode 100644 (file)
index 0000000..599aaee
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/props.ma
@@ -0,0 +1,58 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/props".
+
+include "Lift/fwd.ma".
+
+alias id "nplus_conf" = "cic:/matita/RELATIONAL/NPlus/props/nplus_conf.con".
+
+axiom pippo: \forall x,y. x < y \to y <= x \to False.
+
+theorem lift_conf: \forall q,h,d,t,x. Lift q h d t x \to
+                   \forall y. Lift q h d t y \to
+                   x = y.
+ intros 6. elim H; clear H q h d t x;
+ [ lapply linear lift_sort_fwd to H1.
+   subst. auto
+ | lapply linear lift_lref_fwd to H1. 
+   decompose; subst; 
+   [ auto | destruct H1 | destruct H ]
+ | lapply linear lift_lref_fwd to H2. 
+   decompose; subst;
+   [ destruct H | auto | lapply pippo to H1, H4. decompose ]
+ | lapply linear lift_lref_fwd to H3. 
+   decompose; subst;
+   [ destruct H
+   | lapply linear pippo to H5, H1. decompose 
+   | lapply linear nplus_conf to H2, H4. subst. auto 
+   ]
+
+(* 
+theorem lift_ct_le: \forall q,h,d,t,y. (Lift q h d t y) \to
+                    \forall k,e,x. (Lift q k e t x) \to
+                    \forall z. (Lift q k e y z) \to
+                    e <= d \to \forall d'. (k + d == d') \to
+                    (Lift q h d' x z).
+ intros 6. elim H; clear H q h d t y;
+ [ lapply linear lift_sort_fwd to H1.
+   lapply linear lift_sort_fwd to H2.
+   subst. auto
+ | lapply linear lift_lref_fwd to H1. 
+   lapply linear lift_lref_fwd to H2.
+   decompose; subst;
+   [ auto
+   | auto
+   |  
+ *)
\ No newline at end of file