contribs: some improvements

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

diff --git a/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/props.ma b/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/props.ma
index 9d8749aa55c5b7a325a3a88114cbd76b923733f6..a5c566dab9f3ceb4f3ca68ec17045e6ee1625211 100644 (file)
--- a/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/props.ma
+++ b/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/props.ma
@@ -14,48 +14,114 @@
 
 set "baseuri" "cic:/matita/LAMBDA-TYPES/Unified-Sub/Lift/props".
 
-include "Lift/fwd.ma".
+include "Lift/fun.ma".
 
-theorem lift_conf: \forall l,i,t,x. Lift l i t x \to
-                   \forall y. Lift l i t y \to
-                   x = y.
- intros 5. elim H; clear H i t x;
+theorem lift_comp_ge_1: \forall l1,i1,t1,t2. Lift l1 i1 t1 t2 \to
+                        \forall l2,i2,u1. Lift l2 i2 t1 u1 \to
+                        \forall u2. Lift l2 i2 t2 u2 \to
+                        i1 >= i2 \to \forall i. (l2 + i1 == i) \to
+                        Lift l1 i u1 u2.
+ intros 5. elim H; clear H i1 t1 t2;
+ [ lapply lift_conf to H1, H2. clear H2. subst.
+   lapply linear lift_inv_sort_1 to H1.
+   subst. auto
+ | lapply lift_conf to H2, H3. clear H3. subst.
+   lapply linear lift_inv_lref_1 to H2.
+   decompose; subst; clear H2 H4 i2;
+   [ lapply linear nle_nplus to H5 as H0. clear l2. (**)
+     lapply linear nle_trans to H1, H0.
+     auto
+   | lapply nle_nplus_comp_lt_2 to H3, H5; auto.
+   ]
+ | lapply linear lift_inv_lref_1 to H3.
+   decompose; subst;
+   [ clear H2 H4 H6 n3 l2.
+     lapply linear nle_trans to H3, H5 as H0.
+     lapply linear nle_false to H1, H0. decompose
+   | lapply linear lift_inv_lref_1 to H4.
+     decompose; subst;
+     [ clear H1 H5 H6 H7 n1.
+       lapply linear nle_nplus to H2 as H0. (**)
+       lapply linear nle_trans to H3, H0 as H2.
+       lapply linear nle_false to H2, H4. decompose
+     | clear H3 H4 H5.
+       lapply nle_nplus_comp to H6, H7; auto.
+     ]
+   ]
+ | clear H1 H3.
+   lapply linear lift_inv_bind_1 to H5.
+   lapply linear lift_inv_bind_1 to H6.
+   decompose. subst. auto width = 4
+ | clear H1 H3.
+   lapply linear lift_inv_flat_1 to H5.
+   lapply linear lift_inv_flat_1 to H6.
+   decompose. subst. auto width = 4
+ ].
+qed.
+
+theorem lift_comp_ge_2: \forall l1,i1,t1,t2. Lift l1 i1 t1 t2 \to
+                        \forall l2,i2,u1. Lift l2 i2 t1 u1 \to
+                        \forall i,u2. Lift l2 i t2 u2 \to
+                        i2 >= i1 \to (l1 + i2 == i) \to
+                        Lift l1 i1 u1 u2.
+ intros 5. elim H; clear H i1 t1 t2;
  [ lapply linear lift_inv_sort_1 to H1.
+   lapply linear lift_inv_sort_1 to H2.
    subst. auto
  | lapply linear lift_inv_lref_1 to H2.
-   decompose; subst;
-   [ auto | lapply nle_false to H2, H1. decompose ]
+   lapply linear lift_inv_lref_1 to H3.
+   decompose; subst; (* clear H2 H4 i2; *)
+   [ clear H H3 H4 H5. auto
+   | clear H1 H4 H7.
+     lapply linear nle_nplus to H5 as H0. (**)
+     lapply linear nle_trans to H3, H0 as H2.
+     lapply nle_false to H, H2. decompose
+   | clear H H5 H6.
+     lapply linear nle_trans to H4, H3 as H.
+     lapply nle_false to H, H1. decompose
+   | clear H H2 H5 H7. 
+     lapply linear nle_trans to H4, H3 as H.
+     lapply nle_false to H, H1. decompose
+   ]
+(* 
  | lapply linear lift_inv_lref_1 to H3.
    decompose; subst;
-   [ lapply linear nle_false to H1, H3. decompose
-   | lapply linear nplus_conf to H2, H4. subst. auto
+   [ clear H2 H4 H6 n3 l2.
+     lapply linear nle_trans to H3, H5 as H0.
+     lapply linear nle_false to H1, H0. decompose
+   | lapply linear lift_inv_lref_1 to H4.
+     decompose; subst;
+     [ clear H1 H5 H6 H7 n1.
+       lapply linear nle_nplus to H2 as H0. (**)
+       lapply linear nle_trans to H3, H0 as H2.
+       lapply linear nle_false to H2, H4. decompose
+     | clear H3 H4 H5.
+       lapply nle_nplus_comp to H6, H7; auto.
+     ]
    ]
- | lapply linear lift_inv_bind_1 to H5.
-   decompose. subst. auto.
- | lapply linear lift_inv_flat_1 to H5.
-   decompose. subst. auto.
+ | clear H1 H3.
+   lapply linear lift_inv_bind_1 to H5.
+   lapply linear lift_inv_bind_1 to H6.
+   decompose. subst. auto width = 4
+ | clear H1 H3.
+   lapply linear lift_inv_flat_1 to H5.
+   lapply linear lift_inv_flat_1 to H6.
+   decompose. subst. auto width = 4
  ].
 qed.
 
-alias id "nle_trans" = "cic:/matita/RELATIONAL/NLE/props/nle_trans.con".
-alias id "pippo" = "cic:/matita/RELATIONAL/NLE/nplus/pippo.con".
-alias id "nle_refl" = "cic:/matita/RELATIONAL/NLE/props/nle_refl.con".
 
-theorem lift_ct_le: \forall l1,i1,t,y. (Lift l1 i1 t y) \to
-                    \forall l2,i2,x. (Lift l2 i2 t x) \to
-                    \forall z. (Lift l2 i2 y z) \to
-                    i2 <= i1 \to \forall i. (l2 + i1 == i) \to
-                    (Lift l1 i x z).
- intros 5. elim H; clear H i1 t y;
- [ lapply lift_conf to H1, H2. clear H2. subst.
-   lapply linear lift_inv_sort_1 to H1.
-   subst. auto
- | lapply lift_conf to H2, H3. clear H3. subst.
-   lapply linear lift_inv_lref_1 to H2.
-   decompose; subst; clear H2 H4 i2;
-   [ lapply linear nle_nplus to H5 as H. clear l2. (**)
-     lapply linear nle_trans to H1, H.
-     auto
-   | lapply pippo to H3, H5; [ auto | apply nle_refl | auto ]. (**)
-   ]
- | 
\ No newline at end of file
+(*
+theorem lift_trans_le: \forall l1,i1,t1,t2. Lift l1 i1 t1 t2 \to
+                       \forall l2,i2,z. Lift l2 i2 t2 t3 \to
+                      i1 <= i2 \to 
+                      \forall i. \to i2 <= i \to (l1 + i1 == i) \to
+                      \forall l. (l1 + l2 == l) \to Lift l i1 t1 t3.
+*)
+axiom lift_conf_back_ge: \forall l1,i1,u1,u2. Lift l1 i1 u1 u2 \to
+                        \forall l2,i,t2. Lift l2 i t2 u2 \to
+                        \forall i2. i2 >= i1 \to (l1 + i2 == i) \to
+                         \exists t1. | Lift l2 i2 t1 u1 \land
+                                       Lift l1 i1 t1 t2.
+
+*)