(**************************************************************************)
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 ************************************)
∀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 fpbq_fquq, tri_step/
+/3 width=5 by fquq_fpb, fpbs_strap1/
qed.
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, fpbq_fquq/
+/3 width=5 by fpbs_strap1, fquq_fpb/
qed-.
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, fpbq_fquq/
+/3 width=5 by fpbs_strap2, fquq_fpb/
qed-.