From cfc43911db215e21036317b26bd1dcf9c3e5d435 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Wed, 15 Jan 2014 16:37:48 +0000
Subject: [PATCH] we start a criterion on extended computation

---
 .../basic_2/computation/cpxs_cpys.ma          | 35 +++++++++++++++++++
 .../lambdadelta/basic_2/web/basic_2_src.tbl   |  2 +-
 2 files changed, 36 insertions(+), 1 deletion(-)
 create mode 100644 matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpys.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpys.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpys.ma
new file mode 100644
index 000000000..0bbe9835c
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpys.ma
@@ -0,0 +1,35 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/substitution/cpys_cpys.ma".
+include "basic_2/computation/cpxs_cpxs.ma".
+
+(* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
+
+(* Main properties **********************************************************)
+
+lemma cpx_fwd_cpys_tpxs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 →
+                         ∃∃T. ⦃G, L⦄ ⊢ T1 ▶*×[0, ∞] T & ⦃G, ⋆⦄ ⊢ T ➡*[h, g] T2.
+#h #g #G #L #T1 #T2 #H elim H -G -L -T1 -T2
+[ /2 width=3 by ex2_intro/
+| /4 width=3 by cpx_cpxs, cpx_sort, ex2_intro/
+| #I #G #L #K #V1 #V2 #W2 #i #HLK #_ #HVW2 * #V #HV1 #HV2
+  elim (lift_total V 0 (i+1)) #W #HVW
+  @(ex2_intro … W) /2 width=7 by cpys_subst_Y2/
+| #a #I #G #L #V1 #V2 #T1 #T2 #_ #_ * #V #HV1 #HV2 * #T #HT1 #HT2
+  elim (cpys_split_up … HT1 1) -HT1 // #T0 #HT10 #HT0
+  @(ex2_intro … (ⓑ{a,I}V.T0))
+  [ @(cpys_bind … HV1) -HV1
+  | @(cpxs_bind … HV2) -HV2
+  ]  
diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
index 920657dd2..ceacb2e53 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
@@ -106,7 +106,7 @@ table {
         ]
         [ { "context-sensitive extended computation" * } {
              [ "lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )" "lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?,?] ? )" "lpxs_ldrop" + "lpxs_lleq" + "lpxs_aaa" + "lpxs_cpxs" + "lpxs_lpxs" * ]
-             [ "cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )" "cpxs_tstc" + "cpxs_tstc_vector" + "cpxs_lift" + "cpxs_lleq" + "cpxs_aaa" + "cpxs_cpxs" * ]
+             [ "cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )" "cpxs_tstc" + "cpxs_tstc_vector" + "cpxs_lift" + "cpxs_cpys" + "cpxs_lleq" + "cpxs_aaa" + "cpxs_cpxs" * ]
           }
         ]
         [ { "context-sensitive computation" * } {
-- 
2.39.2