--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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/reducibility/cpr.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL CONVERSION ON TERMS ***************************)
+
+definition cpc: lenv → relation term ≝
+ λL,T1,T2. L ⊢ T1 ➡ T2 ∨ L ⊢ T2 ➡ T1.
+
+interpretation
+ "context-sensitive parallel conversion (term)"
+ 'PConv L T1 T2 = (cpc L T1 T2).
+
+(* Basic properties *********************************************************)
+
+lemma cpc_refl: ∀L. reflexive … (cpc L).
+/2 width=1/ qed.
+
+lemma cpc_sym: ∀L. symmetric … (cpc L).
+#L #T1 #T2 * /2 width=1/
+qed.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma cpc_fwd_cpr: ∀L,T1,T2. L ⊢ T1 ⬌ T2 → ∃∃T. L ⊢ T1 ➡ T & L ⊢ T2 ➡ T.
+#L #T1 #T2 * /2 width=3/
+qed.