+(**************************************************************************)
+(* ___ *)
+(* ||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/static/ffdeq_lfeq.ma".
+include "basic_2/rt_computation/lfpxs_lpxs.ma".
+include "basic_2/rt_computation/fpbs_lfpxs.ma".
+
+(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
+
+(* Properties with uncounted parallel rt-computation on local environments **)
+
+(* Basic_2A1: uses: fpbs_intro_alt *)
+lemma fpbs_intro_star: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
+ ∀G,L,T0. ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄ →
+ ∀L0. ⦃G, L⦄ ⊢ ⬈*[h] L0 →
+ ∀G2,L2,T2. ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ .
+/3 width=9 by fpbs_intro_fstar, lfpxs_lpxs/ qed.
+
+(* Eliminators with uncounted parallel rt-computation on local environments *)
+
+(* Basic_2A1: uses: fpbs_inv_alt *)
+lemma fpbs_inv_star: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
+ ∃∃G,L,L0,T,T0. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T & ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄
+ & ⦃G, L⦄ ⊢ ⬈*[h] L0 & ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H
+elim (fpbs_inv_fstar … H) -H #G #L #L0 #T #T0 #HT1 #H10 #HL0 #H02
+elim (lfpxs_inv_lpxs_lfeq … HL0) -HL0 #L3 #HL3 #HL30
+/3 width=11 by lfeq_lfdeq_trans, ex4_5_intro/
+qed-.