X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Funfold%2Fthin_delift.ma;h=faf9f4506581989e39e0b52312fed0d1986a7bb0;hb=439b6ec33d749ba4e6ae0938e973a85bc23e306e;hp=0653266ee7fc1c818e63109cf4304f75556fafcd;hpb=636c25914e83819c2f529edc891a7eb899499a97;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/basic_2/unfold/thin_delift.ma b/matita/matita/contribs/lambda_delta/basic_2/unfold/thin_delift.ma
index 0653266ee..faf9f4506 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/thin_delift.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/thin_delift.ma
@@ -20,9 +20,9 @@ include "basic_2/unfold/thin.ma".
 
 (* Inversion lemmas on inverse basic term relocation ************************)
 
-lemma thin_inv_delift1: ∀I,K1,V1,L2,d,e. K1. ⓑ{I} V1 [d, e] ≡ L2 → 0 < d →
-                        ∃∃K2,V2. K1 [d - 1, e] ≡ K2 &
-                                 K1 ⊢ V1 [d - 1, e] ≡ V2 &
+lemma thin_inv_delift1: ∀I,K1,V1,L2,d,e. ▼*[d, e] K1. ⓑ{I} V1 ≡ L2 → 0 < d →
+                        ∃∃K2,V2. ▼*[d - 1, e] K1 ≡ K2 &
+                                 K1 ⊢ ▼*[d - 1, e] V1 ≡ V2 &
                                  L2 = K2. ⓑ{I} V2.
 #I #K1 #V1 #L2 #d #e * #X #HK1 #HL2 #e
 elim (ltpss_inv_tpss11 … HK1 ?) -HK1 // #K #V #HK1 #HV1 #H destruct
@@ -32,8 +32,8 @@ qed-.
 
 (* Properties on inverse basic term relocation ******************************)
 
-lemma thin_delift1: ∀L1,L2,d,e. L1 [d, e] ≡ L2 → ∀V1,V2. L1 ⊢ V1 [d, e] ≡ V2 →
-                    ∀I. L1.ⓑ{I}V1 [d + 1, e] ≡ L2.ⓑ{I}V2.
+lemma thin_delift1: ∀L1,L2,d,e. ▼*[d, e] L1 ≡ L2 → ∀V1,V2. L1 ⊢ ▼*[d, e] V1 ≡ V2 →
+                    ∀I. ▼*[d + 1, e] L1.ⓑ{I}V1 ≡ L2.ⓑ{I}V2.
 #L1 #L2 #d #e * #L #HL1 #HL2 #V1 #V2 * #V #HV1 #HV2 #I
 elim (ltpss_tpss_conf … HV1 … HL1) -HV1 #V0 #HV10 #HV0
 elim (tpss_inv_lift1_be … HV0 … HL2 … HV2 ? ?) -HV0 // <minus_n_n #X #H1 #H2
@@ -41,11 +41,11 @@ lapply (tpss_inv_refl_O2 … H1) -H1 #H destruct
 lapply (lift_mono … H2 … HV2) -H2 #H destruct /3 width=5/
 qed.
 
-lemma thin_delift_tpss_conf_le: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶* U2 →
-                                ∀T1,dd,ee. L ⊢ U1 [dd, ee] ≡ T1 →
-                                ∀K. L [dd, ee] ≡ K → d + e ≤ dd →
-                                ∃∃T2. K ⊢ T1 [d, e] ▶* T2 &
-                                      L ⊢ U2 [dd, ee] ≡ T2.
+lemma thin_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 #HUT1 #K * #Y #HLY #HYK #Hdedd
 lapply (delift_ltpss_conf_eq … HUT1 … HLY) -HUT1 #HUT1
 elim (ltpss_tpss_conf … HU12 … HLY) -HU12 #U #HU1 #HU2
@@ -54,19 +54,19 @@ lapply (tpss_delift_trans_eq … HU2 … HUT) -U #HU2T
 lapply (ltpss_delift_trans_eq … HLY … HU2T) -Y /2 width=3/
 qed.
 
-lemma thin_delift_tps_conf_le: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶ U2 →
-                               ∀T1,dd,ee. L ⊢ U1 [dd, ee] ≡ T1 →
-                               ∀K. L [dd, ee] ≡ K → d + e ≤ dd →
-                               ∃∃T2. K ⊢ T1 [d, e] ▶* T2 &
-                                     L ⊢ U2 [dd, ee] ≡ T2.
+lemma thin_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 thin_delift_tpss_conf_le_up: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶* U2 →
-                                   ∀T1,dd,ee. L ⊢ U1 [dd, ee] ≡ T1 →
-                                   ∀K. L [dd, ee] ≡ K →
+lemma thin_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 ⊢ U2 [dd, ee] ≡ T2.
+                                   ∃∃T2. K ⊢ T1 ▶* [d, dd - d] T2 &
+                                         L ⊢ ▼*[dd, ee] U2 ≡ T2.
 #L #U1 #U2 #d #e #HU12 #T1 #dd #ee #HUT1 #K * #Y #HLY #HYK #Hdd #Hdde #Hddee
 lapply (delift_ltpss_conf_eq … HUT1 … HLY) -HUT1 #HUT1
 elim (ltpss_tpss_conf … HU12 … HLY) -HU12 #U #HU1 #HU2
@@ -75,19 +75,19 @@ lapply (tpss_delift_trans_eq … HU2 … HUT) -U #HU2T
 lapply (ltpss_delift_trans_eq … HLY … HU2T) -Y /2 width=3/
 qed.
 
-lemma thin_delift_tps_conf_le_up: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶ U2 →
-                                  ∀T1,dd,ee. L ⊢ U1 [dd, ee] ≡ T1 →
-                                  ∀K. L [dd, ee] ≡ K →
+lemma thin_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 ⊢ U2 [dd, ee] ≡ T2.
-/3 width=6 by thin_delift_tpss_conf_le_up, tpss_strap/ qed. (**) (* too slow without trace *)
+                                  ∃∃T2. K ⊢ T1 ▶* [d, dd - d] T2 &
+                                        L ⊢ ▼*[dd, ee] U2 ≡ T2.
+/3 width=6 by thin_delift_tpss_conf_le_up, tpss_strap2/ qed. (**) (* too slow without trace *)
 
-lemma thin_delift_tpss_conf_be: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶* U2 →
-                                ∀T1,dd,ee. L ⊢ U1 [dd, ee] ≡ T1 →
-                                ∀K. L [dd, ee] ≡ K → d ≤ dd → dd + ee ≤ d + e →
-                                ∃∃T2. K ⊢ T1 [d, e - ee] ▶* T2 &
-                                      L ⊢ U2 [dd, ee] ≡ T2.
+lemma thin_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 ⊢ ▼*[dd, ee] U2 ≡ T2.
 #L #U1 #U2 #d #e #HU12 #T1 #dd #ee #HUT1 #K * #Y #HLY #HYK #Hdd #Hddee
 lapply (delift_ltpss_conf_eq … HUT1 … HLY) -HUT1 #HUT1
 elim (ltpss_tpss_conf … HU12 … HLY) -HU12 #U #HU1 #HU2
@@ -96,9 +96,9 @@ lapply (tpss_delift_trans_eq … HU2 … HUT) -U #HU2T
 lapply (ltpss_delift_trans_eq … HLY … HU2T) -Y /2 width=3/
 qed.
 
-lemma thin_delift_tps_conf_be: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶ U2 →
-                               ∀T1,dd,ee. L ⊢ U1 [dd, ee] ≡ T1 →
-                               ∀K. L [dd, ee] ≡ K → d ≤ dd → dd + ee ≤ d + e →
-                               ∃∃T2. K ⊢ T1 [d, e - ee] ▶* T2 &
-                                     L ⊢ U2 [dd, ee] ≡ T2.
+lemma thin_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 ⊢ ▼*[dd, ee] U2 ≡ T2.
 /3 width=3/ qed.