(* *)
(**************************************************************************)
-include "basic_2/static/ffdeq_fqup.ma".
include "basic_2/rt_computation/cpxs.ma".
include "basic_2/rt_computation/fpbs_fqup.ma".
(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
-(* Properties with uncounted context-sensitive parallel rt-computation ******)
+(* Properties with unbound context-sensitive parallel rt-computation ********)
lemma cpxs_fpbs: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
#h #o #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
/3 width=5 by fpbs_strap2, fpbq_cpx/
qed-.
+lemma cpxs_tdeq_fpbs_trans: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
+ ∀T0. T ≛[h, o] T0 →
+ ∀G2,L2,T2. ⦃G1, L1, T0⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+/3 width=3 by cpxs_fpbs_trans, tdeq_fpbs_trans/ qed-.
+
lemma cpxs_tdeq_fpbs: ∀h,o,G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬈*[h] T →
∀T2. T ≛[h, o] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
-/4 width=3 by cpxs_fpbs_trans, ffdeq_fpbs, tdeq_ffdeq/ qed.
+/4 width=3 by cpxs_fpbs_trans, fdeq_fpbs, tdeq_fdeq/ qed.
(* Properties with star-iterated structural successor for closures **********)