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[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / computation / cprs_lcprs.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "Basic_2/computation/cprs_cprs.ma".
+include "Basic_2/computation/lcprs_lcprs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
+
+(* Properties exploiting context-senstive computation on local environments *)
+
+(* Basic_1: was just: pr3_pr3_pr3_t *)
+lemma lcprs_cprs_trans: ∀L1,L2. L1 ⊢ ➡* L2 →
+                        ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
+#L1 #L2 #HL12 @(lcprs_ind … HL12) -L2 // /3 width=3/
+qed.
+
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_1: was pr3_gen_abbr *)
+lemma cprs_inv_abbr1: ∀L,V1,T1,U2. L ⊢ ⓓV1. T1 ➡* U2 →
+                      (∃∃V2,T2. L ⊢ V1 ➡* V2 & L. ⓓV1 ⊢ T1 ➡* T2 &
+                                U2 = ⓓV2. T2
+                      ) ∨
+                      ∃∃U. ⇧[0, 1] U2 ≡ U & L. ⓓV1 ⊢ T1 ➡* U.
+#L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /3 width=5/
+#U0 #U2 #_ #HU02 * *
+[ #V0 #T0 #HV10 #HT10 #H destruct
+  elim (cpr_inv_abbr1 … HU02) -HU02 *
+  [ #V #V2 #T2 #HV0 #HV2 #HT02 #H destruct
+    lapply (cpr_intro … HV0 … HV2) -HV2 #HV02
+    lapply (ltpr_cpr_trans (L.ⓓV0) … HT02) /2 width=1/ -V #HT02
+    lapply (lcprs_cprs_trans (L. ⓓV1) … HT02) -HT02 /2 width=1/ /4 width=5/
+  | -V0 #T2 #HT20 #HTU2
+    elim (lift_total U2 0 1) #U0 #HU20
+    lapply (cpr_lift (L.ⓓV1) … HT20 … HU20 HTU2) -T2 /2 width=1/ /4 width=5/
+  ]
+| #U1 #HU01 #HTU1
+  elim (lift_total U2 0 1) #U #HU2
+  lapply (cpr_lift (L.ⓓV1) … HU01 … HU2 HU02) -U0 /2 width=1/ /4 width=5/
+]
+qed-.