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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/rt_computation/cpxs.ma".
16 include "basic_2/rt_computation/fpbs_fqup.ma".
18 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
20 (* Properties with extended context-sensitive parallel rt-computation *******)
23 ∀G,L,T1,T2. ❪G,L❫ ⊢ T1 ⬈* T2 → ❪G,L,T1❫ ≥ ❪G,L,T2❫.
24 #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
25 /3 width=5 by fpbq_cpx, fpbs_strap1/
28 lemma fpbs_cpxs_trans:
29 ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
30 ∀T2. ❪G,L❫ ⊢ T ⬈* T2 → ❪G1,L1,T1❫ ≥ ❪G,L,T2❫.
31 #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
32 /3 width=5 by fpbs_strap1, fpbq_cpx/
35 lemma cpxs_fpbs_trans:
36 ∀G1,G2,L1,L2,T,T2. ❪G1,L1,T❫ ≥ ❪G2,L2,T2❫ →
37 ∀T1. ❪G1,L1❫ ⊢ T1 ⬈* T → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
38 #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
39 /3 width=5 by fpbs_strap2, fpbq_cpx/
42 lemma cpxs_teqx_fpbs_trans:
43 ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T → ∀T0. T ≛ T0 →
44 ∀G2,L2,T2. ❪G1,L1,T0❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
45 /3 width=3 by cpxs_fpbs_trans, teqx_fpbs_trans/ qed-.
48 ∀G,L,T1,T. ❪G,L❫ ⊢ T1 ⬈* T →
49 ∀T2. T ≛ T2 → ❪G,L,T1❫ ≥ ❪G,L,T2❫.
50 /4 width=3 by cpxs_fpbs_trans, feqx_fpbs, teqx_feqx/ qed.
52 (* Properties with star-iterated structural successor for closures **********)
55 ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T →
56 ∀G2,L2,T2. ❪G1,L1,T❫ ⬂* ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
57 /3 width=5 by fpbs_fqus_trans, cpxs_fpbs/ qed.
59 (* Properties with plus-iterated structural successor for closures **********)
62 ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T →
63 ∀G2,L2,T2. ❪G1,L1,T❫ ⬂+ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
64 /3 width=5 by fpbs_fqup_trans, cpxs_fpbs/ qed.