--- /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 L2 ⦄ )"
+ non associative with precedence 45
+ for @{ 'FocalizedPConvAlt $L1 $L2 }.
+
+include "basic_2/reducibility/lfpr.ma".
+
+(* FOCALIZED PARALLEL CONVERSION ON LOCAL ENVIRONMENTS **********************)
+
+definition lfpc: relation lenv ≝
+ λL1,L2. ⦃L1⦄ ➡ ⦃L2⦄ ∨ ⦃L2⦄ ➡ ⦃L1⦄.
+
+interpretation
+ "focalized parallel conversion (local environment)"
+ 'FocalizedPConv L1 L2 = (lfpc L1 L2).
+
+(* Basic properties *********************************************************)
+
+lemma lfpc_refl: ∀L. ⦃L⦄ ⬌ ⦃L⦄.
+/2 width=1/ qed.
+
+lemma lfpc_sym: ∀L1,L2. ⦃L1⦄ ⬌ ⦃L2⦄ → ⦃L2⦄ ⬌ ⦃L1⦄.
+#L1 #L2 * /2 width=1/
+qed.
+
+lemma lfpc_lfpr: ∀L1,L2. ⦃L1⦄ ⬌ ⦃L2⦄ → ∃∃L. ⦃L1⦄ ➡ ⦃L⦄ & ⦃L2⦄ ➡ ⦃L⦄.
+#L1 #L2 * /2 width=3/
+qed.