- lambda_delta: subject reduction for nativa type assignment begins ...

[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 c706163a904a1192e639f1933140bd52a1546732..aabd723acd7da929d41ab11b8a5c201324c724e9 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
@@ -20,73 +20,73 @@ include "basic_2/unfold/delift.ma".
 (* 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 →
+                           ∀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.
+                           ∃∃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 →
+                          ∀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.
+                          ∃∃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 →
+                              ∀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 ⊢ 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 →
+                             ∀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 ⊢ 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 →
+                           ∀T1,dd,ee. L ⊢ U1 ▼*[dd, ee] ≡ T1 →
                            ∀K. ⇩[dd, ee] L ≡ K → d ≤ dd → dd + ee ≤ d + e →
                            ∃∃T2. K ⊢ T1 ▶* [d, e - ee] T2 &
-                                 L ⊢ U2 [dd, ee] ≡ T2.
+                                 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 // -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 →
+                          ∀T1,dd,ee. L ⊢ U1 ▼*[dd, ee] ≡ T1 →
                           ∀K. ⇩[dd, ee] L ≡ K → d ≤ dd → dd + ee ≤ d + e →
                           ∃∃T2. K ⊢ T1 ▶* [d, e - ee] T2 &
-                                L ⊢ U2 [dd, ee] ≡ T2.
+                                L ⊢ U2 ▼*[dd, ee] ≡ 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.
+                           ∀T. L ⊢ U1 ▼*[d, e] ≡ T → L ⊢ U2 ▼*[d, e] ≡ 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.
+                          ∀T. L ⊢ U1 ▼*[d, e] ≡ T → L ⊢ U2 ▼*[d, e] ≡ 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.
+                            ∀T. L ⊢ U2 ▼*[d, e] ≡ T → L ⊢ U1 ▼*[d, e] ≡ 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.
+                           ∀T. L ⊢ U2 ▼*[d, e] ≡ T → L ⊢ U1 ▼*[d, e] ≡ T.
 /3 width=3/ qed.