update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / conversion / cpc.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/conversion/cpc.ma b/matita/matita/contribs/lambdadelta/basic_2A/conversion/cpc.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_2A/notation/relations/pconv_4.ma".
+include "basic_2A/reduction/cpr.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL CONVERSION ON TERMS ***************************)
+
+definition cpc: relation4 genv lenv term term ≝
+                λG,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 ∨ ⦃G, L⦄ ⊢ T2 ➡ T1.
+
+interpretation
+   "context-sensitive parallel conversion (term)"
+   'PConv G L T1 T2 = (cpc G L T1 T2).
+
+(* Basic properties *********************************************************)
+
+lemma cpc_refl: ∀G,L. reflexive … (cpc G L).
+/2 width=1 by or_intror/ qed.
+
+lemma cpc_sym: ∀G,L. symmetric … (cpc L G).
+#G #L #T1 #T2 * /2 width=1 by or_introl, or_intror/
+qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma cpc_fwd_cpr: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ∃∃T. ⦃G, L⦄ ⊢ T1 ➡ T & ⦃G, L⦄ ⊢ T2 ➡ T.
+#G #L #T1 #T2 * /2 width=3 by ex2_intro/
+qed-.