(* *)
(**************************************************************************)
-include "basic_2/s_computation/fqus_fqup.ma".
+include "static_2/s_computation/fqus_fqup.ma".
+include "static_2/static/fdeq_fqup.ma".
include "basic_2/rt_computation/fpbs_fqus.ma".
(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
+(* Advanced properties ******************************************************)
+
+lemma tdeq_fpbs_trans: ∀h,o,T1,T. T1 ≛[h, o] T →
+ ∀G1,G2,L1,L2,T2. ⦃G1, L1, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+/3 width=5 by fdeq_fpbs_trans, tdeq_fdeq/ qed-.
+
+lemma fpbs_tdeq_trans: ∀h,o,G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T⦄ →
+ ∀T2. T ≛[h, o] T2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+/3 width=5 by fpbs_fdeq_trans, tdeq_fdeq/ qed-.
+
(* Properties with plus-iterated structural successor for closures **********)
lemma fqup_fpbs: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →