--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( ⦃ term 46 L1 , break term 46 T1 ⦄ ⬌ break ⦃ term 46 L2 , break term 46 T2 ⦄ )"
+ non associative with precedence 45
+ for @{ 'FocalizedPConv $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( ⦃ term 46 L1 , break term 46 T1 ⦄ ⬌ ⬌ break ⦃ term 46 L2 , break term 46 T2 ⦄ )"
+ non associative with precedence 45
+ for @{ 'FocalizedPConvAlt $L1 $T1 $L2 $T2 }.
+
+include "basic_2/reducibility/fpr.ma".
+
+(* CONTEXT-FREE PARALLEL CONVERSION ON CLOSURES *****************************)
+
+definition fpc: bi_relation lenv term ≝
+ λL1,T1,L2,T2. ⦃L1, T1⦄ ➡ ⦃L2, T2⦄ ∨ ⦃L2, T2⦄ ➡ ⦃L1, T1⦄.
+
+interpretation
+ "context-free parallel conversion (closure)"
+ 'FocalizedPConv L1 T1 L2 T2 = (fpc L1 T1 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma fpc_refl: bi_reflexive … fpc.
+/2 width=1/ qed.
+
+lemma fpc_sym: bi_symmetric … fpc.
+#L1 #L2 #T1 #T2 * /2 width=1/
+qed.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma fpc_fwd_fpr: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⬌ ⦃L2, T2⦄ →
+ ∃∃L,T. ⦃L1, T1⦄ ➡ ⦃L, T⦄ & ⦃L2, T2⦄ ➡ ⦃L, T⦄.
+#L1 #L2 #T1 #T2 * /2 width=4/
+qed.