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 "basic_2/rt_computation/cpxs.ma".
16 include "basic_2/rt_computation/fpbs_feqg.ma".
17 include "basic_2/rt_computation/fpbs_fqus.ma".
19 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
21 (* Properties with extended context-sensitive parallel rt-computation *******)
24 ∀G,L,T1,T2. ❨G,L❩ ⊢ T1 ⬈* T2 → ❨G,L,T1❩ ≥ ❨G,L,T2❩.
25 #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
26 /3 width=5 by cpx_fpb, fpbs_strap1/
29 lemma fpbs_cpxs_trans:
30 ∀G1,G,L1,L,T1,T. ❨G1,L1,T1❩ ≥ ❨G,L,T❩ →
31 ∀T2. ❨G,L❩ ⊢ T ⬈* T2 → ❨G1,L1,T1❩ ≥ ❨G,L,T2❩.
32 #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
33 /3 width=5 by fpbs_strap1, cpx_fpb/
36 lemma cpxs_fpbs_trans:
37 ∀G1,G2,L1,L2,T,T2. ❨G1,L1,T❩ ≥ ❨G2,L2,T2❩ →
38 ∀T1. ❨G1,L1❩ ⊢ T1 ⬈* T → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
39 #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
40 /3 width=5 by fpbs_strap2, cpx_fpb/
43 lemma cpxs_teqg_fpbs_trans (S):
44 reflexive … S → symmetric … S →
45 ∀G1,L1,T1,T. ❨G1,L1❩ ⊢ T1 ⬈* T → ∀T0. T ≛[S] T0 →
46 ∀G2,L2,T2. ❨G1,L1,T0❩ ≥ ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
47 /3 width=6 by cpxs_fpbs_trans, teqg_fpbs_trans/ qed-.
49 lemma cpxs_teqg_fpbs (S):
50 reflexive … S → symmetric … S →
51 ∀G,L,T1,T. ❨G,L❩ ⊢ T1 ⬈* T →
52 ∀T2. T ≛[S] T2 → ❨G,L,T1❩ ≥ ❨G,L,T2❩.
53 /4 width=5 by cpxs_fpbs_trans, feqg_fpbs, teqg_feqg/ qed.
55 (* Properties with plus-iterated structural successor for closures **********)
58 ∀G1,L1,T1,T. ❨G1,L1❩ ⊢ T1 ⬈* T →
59 ∀G2,L2,T2. ❨G1,L1,T❩ ⬂+ ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
60 /3 width=5 by fpbs_fqup_trans, cpxs_fpbs/ qed.
62 (* Properties with star-iterated structural successor for closures **********)
65 ∀G1,L1,T1,T. ❨G1,L1❩ ⊢ T1 ⬈* T →
66 ∀G2,L2,T2. ❨G1,L1,T❩ ⬂* ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
67 /3 width=5 by fpbs_fqus_trans, cpxs_fpbs/ qed.