+++ /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/computation/cpxs_lift.ma".
-include "basic_2/computation/fpbs.ma".
-
-(* "QRST" PARALLEL COMPUTATION FOR CLOSURES *********************************)
-
-(* Advanced properties ******************************************************)
-
-lemma lstas_fpbs: ∀h,o,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 →
- ∀d1. d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
-/3 width=5 by cpxs_fpbs, lstas_cpxs/ qed.
-
-lemma sta_fpbs: ∀h,o,G,L,T,U,d.
- ⦃G, L⦄ ⊢ T ▪[h, o] d+1 → ⦃G, L⦄ ⊢ T •*[h, 1] U →
- ⦃G, L, T⦄ ≥[h, o] ⦃G, L, U⦄.
-/2 width=5 by lstas_fpbs/ qed.
-
-(* Note: this is used in the closure proof *)
-lemma cpr_lpr_sta_fpbs: ∀h,o,G,L1,L2,T1,T2,U2,d2.
- ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
- ⦃G, L2⦄ ⊢ T2 ▪[h, o] d2+1 → ⦃G, L2⦄ ⊢ T2 •*[h, 1] U2 →
- ⦃G, L1, T1⦄ ≥[h, o] ⦃G, L2, U2⦄.
-/4 width=5 by fpbs_strap1, cpr_lpr_fpbs, sta_cpx, fpbq_cpx/ qed.