+(**************************************************************************)
+(* ___ *)
+(* ||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-.