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

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpre_cpre.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_cpre.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_cpre.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/cprs_cnr.ma".
+include "basic_2/rt_computation/cprs_cprs.ma".
+include "basic_2/rt_computation/cpre.ma".
+
+(* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL R-TRANSITION ON TERMS *********)
+
+(* Properties with context-sensitive parallel r-computation for terms ******)
+
+lemma cpre_cprs_conf (h) (G) (L) (T):
+      ∀T1. ⦃G,L⦄ ⊢ T ➡*[h] T1 → ∀T2. ⦃G,L⦄ ⊢ T ➡*[h] 𝐍⦃T2⦄ → ⦃G,L⦄ ⊢ T1 ➡*[h] 𝐍⦃T2⦄.
+#h #G #L #T0 #T1 #HT01 #T2 * #HT02 #HT2
+elim (cprs_conf … HT01 … HT02) -T0 #T0 #HT10 #HT20
+lapply (cprs_inv_cnr_sn … HT20 HT2) -HT20 #H destruct
+/2 width=1 by cpme_intro/
+qed-.
+
+(* Main properties *********************************************************)
+
+(* Basic_1: was: nf2_pr3_confluence *)
+theorem cpre_mono (h) (G) (L) (T):
+        ∀T1. ⦃G,L⦄ ⊢ T ➡*[h] 𝐍⦃T1⦄ → ∀T2. ⦃G,L⦄ ⊢ T ➡*[h] 𝐍⦃T2⦄ → T1 = T2.
+#h #G #L #T0 #T1 * #HT01 #HT1 #T2 * #HT02 #HT2
+elim (cprs_conf … HT01 … HT02) -T0 #T0 #HT10 #HT20
+>(cprs_inv_cnr_sn … HT10 HT1) -T1
+>(cprs_inv_cnr_sn … HT20 HT2) -T2 //
+qed-.