X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_equivalence%2Fcpcs_csx.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_equivalence%2Fcpcs_csx.ma;h=f37dc4184719f9c3e5dd485ab3bc78a2fd3c3f13;hb=db020b4218272e2e35641ce3bc3b0a9b3afda899;hp=0000000000000000000000000000000000000000;hpb=d8f6494f48aa08bb32d9d1ac82fc16e9e41b76ac;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_csx.ma
new file mode 100644
index 000000000..f37dc4184
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_csx.ma
@@ -0,0 +1,40 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/rt_computation/cpre_csx.ma".
+include "basic_2/rt_computation/cpre_cpre.ma".
+include "basic_2/rt_equivalence/cpcs_cprs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL R-EQUIVALENCE FOR TERMS ***********************)
+
+(* Properties with strongly normalizing terms for unbound rt-transition *****)
+
+(* Basic_1: was: cpcs_dec *)
+lemma csx_cpcs_dec (h) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ → ∀T2. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T2⦄ →
+      Decidable … (⦃G,L⦄ ⊢ T1 ⬌*[h] T2).
+#h #G #L #T1 #HT1 #T2 #HT2
+elim (cpre_total_csx … HT1) -HT1 #U1 #HTU1
+elim (cpre_total_csx … HT2) -HT2 #U2 #HTU2
+elim (eq_term_dec U1 U2) [ #H destruct | #HnU12 ]
+[ cases HTU1 -HTU1 #HTU1 #_
+  cases HTU2 -HTU2 #HTU2 #_
+  /3 width=3 by cprs_div, or_introl/
+| @or_intror #H
+  elim (cpcs_inv_cprs … H) -H #T0 #HT10 #HT20
+  lapply (cpre_cprs_conf … HT10 … HTU1) -T1 #H1
+  lapply (cpre_cprs_conf … HT20 … HTU2) -T2 #H2
+  /3 width=6 by cpre_mono/
+]
+qed-.