X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Funfold%2Fdelift_tpss.ma;h=cebcf828ea1c4e944ab56971ba7b71e002c8e8b0;hb=1f1ea7bb9e6c34626bcabd4c0142fcde98bcbbe5;hp=b7bc126df8d48e8d78ce0f11be1be18a337e33c9;hpb=fc5a0d62ece398d8547dda0f429b9f1e24bca306;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/basic_2/unfold/delift_tpss.ma b/matita/matita/contribs/lambda_delta/basic_2/unfold/delift_tpss.ma
index b7bc126df..cebcf828e 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/delift_tpss.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/delift_tpss.ma
@@ -15,44 +15,78 @@
 include "basic_2/unfold/tpss_tpss.ma".
 include "basic_2/unfold/delift.ma".
 
-(* INVERSE TERM RELOCATION  *************************************************)
+(* INVERSE BASIC TERM RELOCATION  *******************************************)
 
 (* Properties on partial unfold on terms ************************************)
 
-lemma delift_tpss_conf_be: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶* U2 →
-                           ∀T1,dd,ee. L ⊢ U1 [dd, ee] ≡ T1 →
+lemma delift_tpss_conf_le: ∀L,U1,U2,d,e. L ⊢ U1 ▶* [d, e] U2 →
+                           ∀T1,dd,ee. L ⊢ ▼*[dd, ee] U1 ≡ T1 →
+                           ∀K. ⇩[dd, ee] L ≡ K → d + e ≤ dd →
+                           ∃∃T2. K ⊢ T1 ▶* [d, e] T2 & L ⊢ ▼*[dd, ee] U2 ≡ T2.
+#L #U1 #U2 #d #e #HU12 #T1 #dd #ee * #X1 #HUX1 #HTX1 #K #HLK #H1
+elim (tpss_conf_eq … HU12 … HUX1) -U1 #U1 #HU21 #HXU1
+elim (tpss_inv_lift1_le … HXU1 … HLK … HTX1 ?) -X1 -HLK // -H1 /3 width=5/
+qed.
+
+lemma delift_tps_conf_le: ∀L,U1,U2,d,e. L ⊢ U1 ▶ [d, e] U2 →
+                          ∀T1,dd,ee. L ⊢ ▼*[dd, ee] U1 ≡ T1 →
+                          ∀K. ⇩[dd, ee] L ≡ K → d + e ≤ dd →
+                          ∃∃T2. K ⊢ T1 ▶* [d, e] T2 & L ⊢ ▼*[dd, ee] U2 ≡ T2.
+/3 width=3/ qed.
+
+lemma delift_tpss_conf_le_up: ∀L,U1,U2,d,e. L ⊢ U1 ▶* [d, e] U2 →
+                              ∀T1,dd,ee. L ⊢ ▼*[dd, ee] U1 ≡ T1 →
+                              ∀K. ⇩[dd, ee] L ≡ K →
+                              d ≤ dd → dd ≤ d + e → d + e ≤ dd + ee →
+                              ∃∃T2. K ⊢ T1 ▶* [d, dd - d] T2 &
+                                    L ⊢ ▼*[dd, ee] U2 ≡ T2.
+#L #U1 #U2 #d #e #HU12 #T1 #dd #ee * #X1 #HUX1 #HTX1 #K #HLK #H1 #H2 #H3
+elim (tpss_conf_eq … HU12 … HUX1) -U1 #U1 #HU21 #HXU1
+elim (tpss_inv_lift1_le_up … HXU1 … HLK … HTX1 ? ? ?) -X1 -HLK // -H1 -H2 -H3 /3 width=5/
+qed.
+
+lemma delift_tps_conf_le_up: ∀L,U1,U2,d,e. L ⊢ U1 ▶ [d, e] U2 →
+                             ∀T1,dd,ee. L ⊢ ▼*[dd, ee] U1 ≡ T1 →
+                             ∀K. ⇩[dd, ee] L ≡ K →
+                             d ≤ dd → dd ≤ d + e → d + e ≤ dd + ee →
+                             ∃∃T2. K ⊢ T1 ▶* [d, dd - d] T2 &
+                                   L ⊢ ▼*[dd, ee] U2 ≡ T2.
+/3 width=6/ qed.
+
+lemma delift_tpss_conf_be: ∀L,U1,U2,d,e. L ⊢ U1 ▶* [d, e] U2 →
+                           ∀T1,dd,ee. L ⊢ ▼*[dd, ee] U1 ≡ T1 →
                            ∀K. ⇩[dd, ee] L ≡ K → d ≤ dd → dd + ee ≤ d + e →
-                           ∃∃T2. K ⊢ T1 [d, e - ee] ▶* T2 &
-                                 L ⊢ U2 [dd, ee] ≡ T2.
+                           ∃∃T2. K ⊢ T1 ▶* [d, e - ee] T2 &
+                                 L ⊢ ▼*[dd, ee] U2 ≡ T2.
 #L #U1 #U2 #d #e #HU12 #T1 #dd #ee * #X1 #HUX1 #HTX1 #K #HLK #H1 #H2
 elim (tpss_conf_eq … HU12 … HUX1) -U1 #U1 #HU21 #HXU1
-elim (tpss_inv_lift1_be … HXU1 … HLK … HTX1 ? ?) -X1 -HLK // /3 width=5/
+elim (tpss_inv_lift1_be … HXU1 … HLK … HTX1 ? ?) -X1 -HLK // -H1 -H2 /3 width=5/
 qed.
 
-lemma delift_tps_conf_be: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶ U2 →
-                          ∀T1,dd,ee. L ⊢ U1 [dd, ee] ≡ T1 →
+lemma delift_tps_conf_be: ∀L,U1,U2,d,e. L ⊢ U1 ▶ [d, e] U2 →
+                          ∀T1,dd,ee. L ⊢ ▼*[dd, ee] U1 ≡ T1 →
                           ∀K. ⇩[dd, ee] L ≡ K → d ≤ dd → dd + ee ≤ d + e →
-                          ∃∃T2. K ⊢ T1 [d, e - ee] ▶* T2 &
-                                L ⊢ U2 [dd, ee] ≡ T2.
+                          ∃∃T2. K ⊢ T1 ▶* [d, e - ee] T2 &
+                                L ⊢ ▼*[dd, ee] U2 ≡ T2.
 /3 width=3/ qed.
 
-lemma delift_tpss_conf_eq: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶* U2 →
-                           ∀T. L ⊢ U1 [d, e] ≡ T → L ⊢ U2 [d, e] ≡ T.
+lemma delift_tpss_conf_eq: ∀L,U1,U2,d,e. L ⊢ U1 ▶* [d, e] U2 →
+                           ∀T. L ⊢ ▼*[d, e] U1 ≡ T → L ⊢ ▼*[d, e] U2 ≡ T.
 #L #U1 #U2 #d #e #HU12 #T * #X1 #HUX1 #HTX1
 elim (tpss_conf_eq … HU12 … HUX1) -U1 #U1 #HU21 #HXU1
 lapply (tpss_inv_lift1_eq … HXU1 … HTX1) -HXU1 #H destruct /2 width=3/
 qed.
 
-lemma delift_tps_conf_eq: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶ U2 →
-                          ∀T. L ⊢ U1 [d, e] ≡ T → L ⊢ U2 [d, e] ≡ T.
+lemma delift_tps_conf_eq: ∀L,U1,U2,d,e. L ⊢ U1 ▶ [d, e] U2 →
+                          ∀T. L ⊢ ▼*[d, e] U1 ≡ T → L ⊢ ▼*[d, e] U2 ≡ T.
 /3 width=3/ qed.
 
-lemma tpss_delift_trans_eq: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶* U2 →
-                            ∀T. L ⊢ U2 [d, e] ≡ T → L ⊢ U1 [d, e] ≡ T.
+lemma tpss_delift_trans_eq: ∀L,U1,U2,d,e. L ⊢ U1 ▶* [d, e] U2 →
+                            ∀T. L ⊢ ▼*[d, e] U2 ≡ T → L ⊢ ▼*[d, e] U1 ≡ T.
 #L #U1 #U2 #d #e #HU12 #T * #X1 #HUX1 #HTX1
 lapply (tpss_trans_eq … HU12 … HUX1) -U2 /2 width=3/
 qed.
 
-lemma tps_delift_trans_eq: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶ U2 →
-                           ∀T. L ⊢ U2 [d, e] ≡ T → L ⊢ U1 [d, e] ≡ T.
+lemma tps_delift_trans_eq: ∀L,U1,U2,d,e. L ⊢ U1 ▶ [d, e] U2 →
+                           ∀T. L ⊢ ▼*[d, e] U2 ≡ T → L ⊢ ▼*[d, e] U1 ≡ T.
 /3 width=3/ qed.