From bf2b1df641df98a3b614a8c3d53edee8beb0964a Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Mon, 8 Apr 2019 18:47:22 +0200
Subject: [PATCH] update in basic_2

+ decidability of cpes
+ some renaming
---
 .../lambdadelta/basic_2/dynamic/cnv_aaa.ma    |  2 +-
 .../basic_2/dynamic/cnv_cpes_dec.ma           | 41 +++++++++++++++++++
 .../lambdadelta/basic_2/dynamic/cnv_cpme.ma   | 30 ++++++++++++++
 .../basic_2/rt_computation/cpme_aaa.ma        | 32 +++++++++++++++
 .../basic_2/rt_computation/cpms_aaa.ma        |  2 +-
 .../basic_2/rt_computation/cpre_cpms.ma       | 27 ++++++++++++
 .../basic_2/rt_computation/cpre_csx.ma        |  2 +-
 .../basic_2/rt_equivalence/cpes_aaa.ma        |  2 +-
 .../lambdadelta/basic_2/web/basic_2_src.tbl   |  6 +--
 9 files changed, 137 insertions(+), 7 deletions(-)
 create mode 100644 matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpes_dec.ma
 create mode 100644 matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpme.ma
 create mode 100644 matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpme_aaa.ma
 create mode 100644 matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_cpms.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
index d8981613d..cad9f2318 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
@@ -56,5 +56,5 @@ lemma cnv_fwd_cpms_total (a) (h) (n) (G) (L):
       ∀T. ⦃G, L⦄ ⊢ T ![a, h] → ∃U. ⦃G,L⦄ ⊢ T ➡*[n,h] U.
 #a #h #n #G #L #T #H
 elim (cnv_fwd_aaa … H) -H #A #HA
-/2 width=2 by aaa_cpms_total/
+/2 width=2 by cpms_total_aaa/
 qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpes_dec.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpes_dec.ma
new file mode 100644
index 000000000..60fc0d0da
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpes_dec.ma
@@ -0,0 +1,41 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/cpme_aaa.ma".
+include "basic_2/rt_computation/cpre_cpre.ma".
+include "basic_2/rt_equivalence/cpes.ma".
+include "basic_2/dynamic/cnv_cpme.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Properties with t-bound rt-equivalence for terms *************************)
+
+lemma cnv_cpes_dec (a) (h) (n1) (n2) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] → ∀T2. ⦃G,L⦄ ⊢ T2 ![a,h] →
+      Decidable … (⦃G,L⦄ ⊢ T1 ⬌*[h,n1,n2] T2).
+#a #h #n1 #n2 #G #L #T1 #HT1 #T2 #HT2
+elim (cnv_fwd_aaa … HT1) #A1 #HA1
+elim (cnv_fwd_aaa … HT2) #A2 #HA2
+elim (cpme_total_aaa h n1 … HA1) -HA1 #U1 #HTU1
+elim (cpme_total_aaa h n2 … HA2) -HA2 #U2 #HTU2
+elim (eq_term_dec U1 U2) [ #H destruct | #HnU12 ]
+[ cases HTU1 -HTU1 #HTU1 #_
+  cases HTU2 -HTU2 #HTU2 #_
+  /3 width=3 by cpms_div, or_introl/
+| @or_intror * #T0 #HT10 #HT20
+  lapply (cnv_cpme_cpms_conf … HT1 … HT10 … HTU1) -T1 #H1
+  lapply (cnv_cpme_cpms_conf … HT2 … HT20 … HTU2) -T2 #H2
+  /3 width=6 by cpre_mono/
+]
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpme.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpme.ma
new file mode 100644
index 000000000..dd3d99a30
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpme.ma
@@ -0,0 +1,30 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/cprs_cnr.ma".
+include "basic_2/rt_computation/cpre.ma".
+include "basic_2/dynamic/cnv_preserve.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Properties with evaluation for t-bound rt-transition on terms ************)
+
+lemma cnv_cpme_cpms_conf (a) (h) (n) (G) (L):
+      ∀T. ⦃G,L⦄ ⊢ T ![a,h] → ∀T1. ⦃G,L⦄ ⊢ T ➡*[n,h] T1 →
+      ∀T2. ⦃G,L⦄ ⊢ T ➡*[h,n] 𝐍⦃T2⦄ → ⦃G,L⦄ ⊢ T1 ➡*[h] 𝐍⦃T2⦄.
+#a #h #n #G #L #T0 #HT0 #T1 #HT01 #T2 * #HT02 #HT2
+elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 <minus_n_n #T0 #HT10 #HT20
+lapply (cprs_inv_cnr_sn … HT20 HT2) -HT20 #H destruct
+/2 width=1 by conj/
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpme_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpme_aaa.ma
new file mode 100644
index 000000000..6d6182540
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpme_aaa.ma
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/csx_aaa.ma".
+include "basic_2/rt_computation/cpms_aaa.ma".
+include "basic_2/rt_computation/cpre_csx.ma".
+include "basic_2/rt_computation/cpre_cpms.ma".
+
+(* EVALUATION FOR T-BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ON TERMS *)
+
+(* Properties with atomic atomic arity assignment on terms ******************)
+
+lemma cpme_total_aaa (h) (n) (A) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ T1 ⁝ A → ∃T2. ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍⦃T2⦄.
+#h #n #A #G #L #T1 #HT1
+elim (cpms_total_aaa h … n … HT1) #T0 #HT10
+elim (cpre_total_csx h G L T0)
+[ #T2 /3 width=4 by cpms_cpre_trans, ex_intro/
+| /4 width=4 by cpms_fwd_cpxs, aaa_csx, csx_cpxs_trans/
+]
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_aaa.ma
index 08f2039c8..41d134080 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_aaa.ma
@@ -25,7 +25,7 @@ include "basic_2/rt_computation/cpms_cpxs.ma".
 lemma cpms_aaa_conf (n) (h): ∀G,L. Conf3 … (aaa G L) (cpms h G L n).
 /3 width=5 by cpms_fwd_cpxs, cpxs_aaa_conf/ qed-.
 
-lemma aaa_cpms_total (h) (G) (L) (n) (A):
+lemma cpms_total_aaa (h) (G) (L) (n) (A):
       ∀T. ⦃G, L⦄ ⊢ T ⁝ A → ∃U. ⦃G,L⦄ ⊢ T ➡*[n,h] U.
 #h #G #L #n elim n -n
 [ /2 width=3 by ex_intro/
diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_cpms.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_cpms.ma
new file mode 100644
index 000000000..a6fc27e18
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_cpms.ma
@@ -0,0 +1,27 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/cpms_cpms.ma".
+include "basic_2/rt_computation/cpre.ma".
+
+(* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL R-TRANSITION ON TERMS **********)
+
+(* Properties with t-bound rt-computarion on terms **************************)
+
+lemma cpms_cpre_trans (h) (n) (G) (L):
+      ∀T1,T0. ⦃G,L⦄ ⊢T1 ➡*[n,h] T0 →
+      ∀T2. ⦃G,L⦄ ⊢ T0 ➡*[h] 𝐍⦃T2⦄ → ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍⦃T2⦄.
+#h #n #G #L #T1 #T0 #HT10 #T2 * #HT02 #HT2
+/3 width=3 by cpms_cprs_trans, conj/
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_csx.ma
index 9b01da5ae..1b1e44804 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_csx.ma
@@ -22,7 +22,7 @@ include "basic_2/rt_computation/cpre.ma".
 (* Properties with strong normalization for unbound rt-transition for terms *)
 
 (* Basic_1: was just: nf2_sn3 *)
-lemma csx_cpre (h) (G) (L):
+lemma cpre_total_csx (h) (G) (L):
       ∀T1. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ → ∃T2. ⦃G, L⦄ ⊢ T1 ➡*[h] 𝐍⦃T2⦄.
 #h #G #L #T1 #H
 @(csx_ind … H) -T1 #T1 #_ #IHT1
diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpes_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpes_aaa.ma
index aae663c8f..2aa50131f 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpes_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpes_aaa.ma
@@ -23,7 +23,7 @@ include "basic_2/rt_equivalence/cpes.ma".
 lemma cpes_refl_aaa (h) (n):
       ∀G,L,T,A.  ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ T ⬌*[h,n,n] T.
 #h #n #G #L #T #A #HA
-elim (aaa_cpms_total h … n … HA) #U #HTU
+elim (cpms_total_aaa h … n … HA) #U #HTU
 /2 width=3 by cpms_div/
 qed.
 
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 57e605d70..76da17d40 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
@@ -25,7 +25,7 @@ table {
         ]
         [ { "context-sensitive native validity" * } {
              [ [ "restricted refinement for lenvs" ] "lsubv ( ? ⊢ ? ⫃![?,?] ? )" "lsubv_drops" + "lsubv_lsubr" + "lsubv_lsuba" + "lsubv_cpms" + "lsubv_cpcs" + "lsubv_cnv" + "lsubv_lsubv" * ]
-             [ [ "for terms" ] "cnv" + "( ⦃?,?⦄ ⊢ ? ![?,?] )" + "( ⦃?,?⦄ ⊢ ? ![?] )" + "( ⦃?,?⦄ ⊢ ? !*[?] )" "cnv_drops" + "cnv_fqus" + "cnv_aaa" + "cnv_fsb" + "cnv_cpm_trans" + "cnv_cpm_conf" + "cnv_cpm_tdeq" + "cnv_cpm_tdeq_trans" + "cnv_cpm_tdeq_conf" + "cnv_cpms_tdeq" + "cnv_cpms_conf" + "cnv_cpms_tdeq_conf" + "cnv_cpes" + "cnv_cpcs" + "cnv_preserve_sub" + "cnv_preserve" * ]
+             [ [ "for terms" ] "cnv" + "( ⦃?,?⦄ ⊢ ? ![?,?] )" + "( ⦃?,?⦄ ⊢ ? ![?] )" + "( ⦃?,?⦄ ⊢ ? !*[?] )" "cnv_drops" + "cnv_fqus" + "cnv_aaa" + "cnv_fsb" + "cnv_cpm_trans" + "cnv_cpm_conf" + "cnv_cpm_tdeq" + "cnv_cpm_tdeq_trans" + "cnv_cpm_tdeq_conf" + "cnv_cpms_tdeq" + "cnv_cpms_conf" + "cnv_cpms_tdeq_conf" + "cnv_cpme" + "cnv_cpes" + "cnv_cpes_dec" + "cnv_cpcs" + "cnv_preserve_sub" + "cnv_preserve" * ]
           }
         ]
      }
@@ -59,14 +59,14 @@ table {
    class "sky"
    [ { "rt-computation" * } {
         [ { "context-sensitive parallel r-computation" * } {
-             [ [ "evaluation for terms" ] "cpre ( ⦃?,?⦄ ⊢ ? ➡*[?] 𝐍⦃?⦄ )" "cpre_cpx" + "cpre_cpre" * ]
+             [ [ "evaluation for terms" ] "cpre ( ⦃?,?⦄ ⊢ ? ➡*[?] 𝐍⦃?⦄ )" "cpre_csx" + "cpre_cpms" + "cpre_cpre" * ]
              [ [ "for lenvs on all entries" ] "lprs ( ⦃?,?⦄ ⊢ ➡*[?] ? )" "lprs_tc" + "lprs_ctc" + "lprs_length" + "lprs_drops" + "lprs_aaa" + "lprs_lpr" + "lprs_lpxs" + "lprs_cpms" + "lprs_cprs" + "lprs_lprs" * ]
              [ [ "for binders" ] "cprs_ext" + "( ⦃?,?⦄ ⊢ ? ➡*[?] ?)" * ]
              [ [ "for terms" ] "cprs" + "( ⦃?,?⦄ ⊢ ? ➡*[?] ?)" "cprs_ctc" + "cprs_drops" + "cprs_cpr" + "cprs_lpr" + "cprs_cnr" + "cprs_cprs" * ]
           }
         ]
         [ { "t-bound context-sensitive parallel rt-computation" * } {
-             [ [ "evaluation for terms" ] "cpme ( ⦃?,?⦄ ⊢ ? ➡*[?,?] 𝐍⦃?⦄ )" * ]
+             [ [ "evaluation for terms" ] "cpme ( ⦃?,?⦄ ⊢ ? ➡*[?,?] 𝐍⦃?⦄ )" "cpme_aaa" * ]
              [ [ "for terms" ] "cpms" + "( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )" "cpms_drops" + "cpms_lsubr" + "cpms_rdeq" + "cpms_aaa" + "cpms_cwhx" + "cpms_lpr" + "cpms_cpxs" + "cpms_fpbs" + "cpms_fpbg" + "cpms_cpms" * ]
           }
         ]
-- 
2.39.2