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