milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / cpr / tprs_tprs.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/tprs_tprs.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/tprs_tprs.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/tprs_tprs.etc
@@ -0,0 +1,43 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/tpr_tpr.ma".
+include "basic_2/computation/tprs.ma".
+
+(* CONTEXT-FREE PARALLEL COMPUTATION ON TERMS *******************************)
+
+(* Advanced properties ******************************************************)
+
+(* Basic_1: was: pr1_strip *)
+lemma tprs_strip: ∀T1,T. T ➡* T1 → ∀T2. T ➡ T2 →
+                  ∃∃T0. T1 ➡ T0 & T2 ➡* T0.
+/3 width=3 by TC_strip1, tpr_conf/ qed.
+
+(* Main propertis ***********************************************************)
+
+(* Basic_1: was: pr1_confluence *)
+theorem tprs_conf: confluent … tprs.
+/3 width=3/ qed.
+
+(* Basic_1: was: pr1_t *)
+theorem tprs_trans: Transitive … tprs.
+/2 width=3/ qed.
+
+(* Basic_1: was: pr1_comp *)
+lemma tprs_pair: ∀I,V1,V2. V1 ➡* V2 → ∀T1,T2. T1 ➡* T2 →
+                 ②{I} V1. T1 ➡* ②{I} V2. T2.
+#I #V1 #V2 #H @(tprs_ind … H) -V2 /2 width=1/
+#V #V2 #_ #HV2 #IHV1 #T1 #T2 #HT12
+@(tprs_trans … (②{I}V.T2)) /2 width=1/
+qed.