(* *)
(**************************************************************************)
-include "basic_2/s_computation/fqus_fqup.ma".
-include "basic_2/static/ffdeq_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 ffdeq_fpbs_trans, tdeq_ffdeq/ qed-.
+lemma tdeq_fpbs_trans: ∀h,T1,T. T1 ≛ T →
+ ∀G1,G2,L1,L2,T2. ⦃G1,L1,T⦄ ≥[h] ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃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_ffdeq_trans, tdeq_ffdeq/ qed-.
+lemma fpbs_tdeq_trans: ∀h,G1,G2,L1,L2,T1,T. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T⦄ →
+ ∀T2. T ≛ T2 → ⦃G1,L1,T1⦄ ≥[h] ⦃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⦄ →
- ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+lemma fqup_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 @(fqup_ind … H) -G2 -L2 -T2
/4 width=5 by fqu_fquq, fpbq_fquq, tri_step/
qed.
-lemma fpbs_fqup_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⦄.
+lemma fpbs_fqup_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⦄.
/3 width=5 by fpbs_fqus_trans, fqup_fqus/ qed-.
-lemma fqup_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⦄.
+lemma fqup_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⦄.
/3 width=5 by fqus_fpbs_trans, fqup_fqus/ qed-.