- intermediate commit to allow debugging of auto tactic in xprs.ma

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

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 a28bf53e8b6ea054704a1ec53ea5e5d450ed8f6e..faf9f4506581989e39e0b52312fed0d1986a7bb0 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/thin_delift.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/thin_delift.ma
@@ -16,12 +16,24 @@ include "basic_2/unfold/delift_tpss.ma".
 include "basic_2/unfold/delift_ltpss.ma".
 include "basic_2/unfold/thin.ma".
 
-(* DELIFT ON LOCAL ENVIRONMENTS *********************************************)
+(* BASIC DELIFT ON LOCAL ENVIRONMENTS ***************************************)
 
-(* Properties on inverse term relocation ************************************)
+(* Inversion lemmas 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_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
+elim (ldrop_inv_skip1 … HL2 ?) -HL2 // #K2 #V2 #HK2 #HV2 #H destruct
+lapply (ltpss_tpss_trans_eq … HV1 … HK1) -HV1 /3 width=5/
+qed-.
+
+(* Properties on inverse basic term relocation ******************************)
+
+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
@@ -29,11 +41,53 @@ 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_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_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
+elim (delift_tpss_conf_le … HU1 … HUT1 … HYK ?) -HU1 -HUT1 // -Hdedd #T #HT1 #HUT
+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 ⊢ ▼*[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 ⊢ ▼*[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 #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
+elim (delift_tpss_conf_le_up … HU1 … HUT1 … HYK ? ? ?) -HU1 -HUT1 // -Hdd -Hdde -Hddee #T #HT1 #HUT
+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 ⊢ ▼*[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 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 ⊢ ▼*[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
@@ -42,9 +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.