We are decapitalizing the contributions' names ...

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_lift.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_lift.ma
new file mode 100644 (file)
index 0000000..ccff2f1
--- /dev/null
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_lift.ma
@@ -0,0 +1,42 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/reducibility/cpr_lift.ma".
+include "Basic_2/computation/cprs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
+
+(* Relocation properties ****************************************************)
+
+(* Basic_1: was: pr3_lift *)
+lemma cprs_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K → ∀T1,U1. ⇧[d, e] T1 ≡ U1 →
+                 ∀T2. K ⊢ T1 ➡* T2 → ∀U2. ⇧[d, e] T2 ≡ U2 →
+                 L ⊢ U1 ➡* U2.
+#L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #HT12 @(cprs_ind … HT12) -T2
+[ -HLK #T2 #HT12
+   <(lift_mono … HTU1 … HT12) -T1 //
+| -HTU1 #T #T2 #_ #HT2 #IHT2 #U2 #HTU2
+  elim (lift_total T d e) #U #HTU
+  lapply (cpr_lift … HLK … HTU … HTU2 … HT2) -T2 -HLK /3 width=3/
+]
+qed.
+
+(* Basic_1: was: pr3_gen_lift *)
+lemma cprs_inv_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K →
+                     ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀U2. L ⊢ U1 ➡* U2 →
+                     ∃∃T2. ⇧[d, e] T2 ≡ U2 & K ⊢ T1 ➡* T2.
+#L #K #d #e #HLK #T1 #U1 #HTU1 #U2 #HU12 @(cprs_ind … HU12) -U2 /2 width=3/
+-HTU1 #U #U2 #_ #HU2 * #T #HTU #HT1
+elim (cpr_inv_lift … HLK … HTU … HU2) -U -HLK /3 width=5/
+qed.