(**************************************************************************)
include "static_2/s_computation/fqus.ma".
-include "basic_2/rt_computation/fpbs.ma".
+include "basic_2/rt_computation/fpbs_fqup.ma".
(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
(* Properties with star-iterated structural successor for closures **********)
-lemma fqus_fpbs: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐* ⦃G2,L2,T2⦄ →
- ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
-/3 width=5 by fpbq_fquq, tri_step/
+lemma fqus_fpbs:
+ ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂* ❨G2,L2,T2❩ →
+ ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
+#G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
+/3 width=5 by fquq_fpb, fpbs_strap1/
qed.
-lemma fpbs_fqus_trans: ∀h,G1,G,L1,L,T1,T. ⦃G1,L1,T1⦄ ≥[h] ⦃G,L,T⦄ →
- ∀G2,L2,T2. ⦃G,L,T⦄ ⊐* ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
-#h #G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
-/3 width=5 by fpbs_strap1, fpbq_fquq/
+lemma fpbs_fqus_trans:
+ ∀G1,G,L1,L,T1,T. ❨G1,L1,T1❩ ≥ ❨G,L,T❩ →
+ ∀G2,L2,T2. ❨G,L,T❩ ⬂* ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
+#G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
+/3 width=5 by fpbs_strap1, fquq_fpb/
qed-.
-lemma fqus_fpbs_trans: ∀h,G,G2,L,L2,T,T2. ⦃G,L,T⦄ ≥[h] ⦃G2,L2,T2⦄ →
- ∀G1,L1,T1. ⦃G1,L1,T1⦄ ⊐* ⦃G,L,T⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
-#h #G #G2 #L #L2 #T #T2 #H1 #G1 #L1 #T1 #H @(fqus_ind_dx … H) -G1 -L1 -T1
-/3 width=5 by fpbs_strap2, fpbq_fquq/
+lemma fqus_fpbs_trans:
+ ∀G,G2,L,L2,T,T2. ❨G,L,T❩ ≥ ❨G2,L2,T2❩ →
+ ∀G1,L1,T1. ❨G1,L1,T1❩ ⬂* ❨G,L,T❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
+#G #G2 #L #L2 #T #T2 #H1 #G1 #L1 #T1 #H @(fqus_ind_dx … H) -G1 -L1 -T1
+/3 width=5 by fpbs_strap2, fquq_fpb/
qed-.