Merge branch 'matita-lablgtk3' of ssh://matita.cs.unibo.it:/srv/git/helm into matita...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / cnv_preserve_cpes.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_cpes.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_cpes.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 (h) (a) (n1) (n2) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![h,a] → ∀T2. ⦃G,L⦄ ⊢ T2 ![h,a] →
+      Decidable … (⦃G,L⦄ ⊢ T1 ⬌*[h,n1,n2] T2).
+#h #a #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-.