update in ground_2 static_2 basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_equivalence / cpes.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpes.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/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/notation/relations/pconvstar_7.ma".
+include "basic_2/rt_computation/cpms.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-EQUIVALENCE FOR TERMS **************)
+
+(* Basic_2A1: uses: scpes *)
+definition cpes (h) (n1) (n2): relation4 genv lenv term term ≝
+           λG,L,T1,T2.
+           ∃∃T. ⦃G, L⦄ ⊢ T1 ➡*[n1,h] T & ⦃G, L⦄ ⊢ T2 ➡*[n2,h] T.
+
+interpretation "t-bound context-sensitive parallel rt-equivalence (term)"
+   'PConvStar h n1 n2 G L T1 T2 = (cpes h n1 n2 G L T1 T2).
+
+(* Basic properties *********************************************************)
+
+(* Basic_2A1: uses: scpds_div *)
+lemma cpms_div (h) (n1) (n2):
+      ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡*[n1,h] T →
+      ∀T2. ⦃G, L⦄ ⊢ T2 ➡*[n2,h] T → ⦃G, L⦄ ⊢ T1 ⬌*[h,n1,n2] T2.
+/2 width=3 by ex2_intro/ qed.
+
+lemma cpes_refl (h): ∀G,L. reflexive … (cpes h 0 0 G L).
+/2 width=3 by cpms_div/ qed.
+
+(* Basic_2A1: uses: scpes_sym *)
+lemma cpes_sym (h) (n1) (n2):
+      ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌*[h,n1,n2] T2 → ⦃G, L⦄ ⊢ T2 ⬌*[h,n2,n1] T1.
+#h #n1 #n2 #G #L #T1 #T2 * /2 width=3 by cpms_div/
+qed-.