- lib: some additions

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / unfold / delift_tpss.ma

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 b7bc126df8d48e8d78ce0f11be1be18a337e33c9..5ba077c6d45bb7d6b478f25558702650a85f7c8e 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/delift_tpss.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/delift_tpss.ma
@@ -15,10 +15,44 @@
 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_le: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶* U2 →
+                           ∀T1,dd,ee. L ⊢ U1 [dd, ee] ≡ T1 →
+                           ∀K. ⇩[dd, ee] L ≡ K → d + e ≤ dd →
+                           ∃∃T2. K ⊢ T1 [d, e] ▶* T2 & L ⊢ U2 [dd, ee] ≡ 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 ⊢ U1 [dd, ee] ≡ T1 →
+                          ∀K. ⇩[dd, ee] L ≡ K → d + e ≤ dd →
+                          ∃∃T2. K ⊢ T1 [d, e] ▶* T2 & L ⊢ U2 [dd, ee] ≡ 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 ⊢ U1 [dd, ee] ≡ T1 →
+                              ∀K. ⇩[dd, ee] L ≡ K →
+                              d ≤ dd → dd ≤ d + e → d + e ≤ dd + ee →
+                              ∃∃T2. K ⊢ T1 [d, dd - d] ▶* T2 &
+                                    L ⊢ U2 [dd, ee] ≡ 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 ⊢ U1 [dd, ee] ≡ T1 →
+                             ∀K. ⇩[dd, ee] L ≡ K →
+                             d ≤ dd → dd ≤ d + e → d + e ≤ dd + ee →
+                             ∃∃T2. K ⊢ T1 [d, dd - d] ▶* T2 &
+                                   L ⊢ U2 [dd, ee] ≡ T2.
+/3 width=6/ qed.
+
 lemma delift_tpss_conf_be: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶* U2 →
                            ∀T1,dd,ee. L ⊢ U1 [dd, ee] ≡ T1 →
                            ∀K. ⇩[dd, ee] L ≡ K → d ≤ dd → dd + ee ≤ d + e →
@@ -26,7 +60,7 @@ lemma delift_tpss_conf_be: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶* U2 →
                                  L ⊢ U2 [dd, ee] ≡ 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 →