--- /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/notation/relations/btpredstarproper_8.ma".
+include "basic_2/computation/fpbc.ma".
+
+(* GENEARAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES *************)
+
+(* Note: this is not transitive *)
+inductive fpbg (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
+| fpbg_cpxs: ∀L2,T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → ⦃G1, L1⦄ ⊢ ➡*[h, g] L2 →
+ fpbg h g G1 L1 T1 G1 L2 T2
+| fpbg_fqup: ∀G2,L,L2,T,T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T → ⦃G1, L1, T⦄ ⊃+ ⦃G2, L, T2⦄ → ⦃G2, L⦄ ⊢ ➡*[h, g] L2 →
+ fpbg h g G1 L1 T1 G2 L2 T2
+| fpbg_lpxs: ∀G2,L,L0,L2,T,T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T → ⦃G1, L1, T⦄ ⊃* ⦃G2, L, T2⦄ → ⦃G2, L⦄ ⊢ ➡*[h, g] L0 →
+ (L ⋕[0, T2] L0 → ⊥) → ⦃G2, L0⦄ ⊢ ➡*[h, g] L2 → L0 ⋕[0, T2] L2 →
+ fpbg h g G1 L1 T1 G2 L2 T2
+.
+
+interpretation "'big tree' proper parallel computation (closure)"
+ 'BTPRedStarProper h g G1 L1 T1 G2 L2 T2 = (fpbg h g G1 L1 T1 G2 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma fpbc_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
+ ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
+/3 width=9 by fpbg_fqup, fpbg_cpxs, fpbg_lpxs/
+qed.