1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "static_2/s_computation/fqus_fqup.ma".
16 include "static_2/static/fdeq_fqup.ma".
17 include "basic_2/rt_computation/fpbs_fqus.ma".
19 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
21 (* Advanced properties ******************************************************)
23 lemma tdeq_fpbs_trans: ∀h,T1,T. T1 ≛ T →
24 ∀G1,G2,L1,L2,T2. ⦃G1,L1,T⦄ ≥[h] ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
25 /3 width=5 by fdeq_fpbs_trans, tdeq_fdeq/ qed-.
27 lemma fpbs_tdeq_trans: ∀h,G1,G2,L1,L2,T1,T. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T⦄ →
28 ∀T2. T ≛ T2 → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
29 /3 width=5 by fpbs_fdeq_trans, tdeq_fdeq/ qed-.
31 (* Properties with plus-iterated structural successor for closures **********)
33 lemma fqup_fpbs: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐+ ⦃G2,L2,T2⦄ →
34 ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
35 #h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
36 /4 width=5 by fqu_fquq, fpbq_fquq, tri_step/
39 lemma fpbs_fqup_trans: ∀h,G1,G,L1,L,T1,T. ⦃G1,L1,T1⦄ ≥[h] ⦃G,L,T⦄ →
40 ∀G2,L2,T2. ⦃G,L,T⦄ ⊐+ ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
41 /3 width=5 by fpbs_fqus_trans, fqup_fqus/ qed-.
43 lemma fqup_fpbs_trans: ∀h,G,G2,L,L2,T,T2. ⦃G,L,T⦄ ≥[h] ⦃G2,L2,T2⦄ →
44 ∀G1,L1,T1. ⦃G1,L1,T1⦄ ⊐+ ⦃G,L,T⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
45 /3 width=5 by fqus_fpbs_trans, fqup_fqus/ qed-.