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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 unbound context-sensitive parallel rt-computation ********)
22 lemma cpxs_fpbs: ∀h,G,L,T1,T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → ❪G,L,T1❫ ≥[h] ❪G,L,T2❫.
23 #h #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
24 /3 width=5 by fpbq_cpx, fpbs_strap1/
27 lemma fpbs_cpxs_trans: ∀h,G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥[h] ❪G,L,T❫ →
28 ∀T2. ❪G,L❫ ⊢ T ⬈*[h] T2 → ❪G1,L1,T1❫ ≥[h] ❪G,L,T2❫.
29 #h #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
30 /3 width=5 by fpbs_strap1, fpbq_cpx/
33 lemma cpxs_fpbs_trans: ∀h,G1,G2,L1,L2,T,T2. ❪G1,L1,T❫ ≥[h] ❪G2,L2,T2❫ →
34 ∀T1. ❪G1,L1❫ ⊢ T1 ⬈*[h] T → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
35 #h #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
36 /3 width=5 by fpbs_strap2, fpbq_cpx/
39 lemma cpxs_teqx_fpbs_trans: ∀h,G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈*[h] T →
41 ∀G2,L2,T2. ❪G1,L1,T0❫ ≥[h] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
42 /3 width=3 by cpxs_fpbs_trans, teqx_fpbs_trans/ qed-.
44 lemma cpxs_teqx_fpbs: ∀h,G,L,T1,T. ❪G,L❫ ⊢ T1 ⬈*[h] T →
45 ∀T2. T ≛ T2 → ❪G,L,T1❫ ≥[h] ❪G,L,T2❫.
46 /4 width=3 by cpxs_fpbs_trans, feqx_fpbs, teqx_feqx/ qed.
48 (* Properties with star-iterated structural successor for closures **********)
50 lemma cpxs_fqus_fpbs: ∀h,G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈*[h] T →
51 ∀G2,L2,T2. ❪G1,L1,T❫ ⬂* ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
52 /3 width=5 by fpbs_fqus_trans, cpxs_fpbs/ qed.
54 (* Properties with plus-iterated structural successor for closures **********)
56 lemma cpxs_fqup_fpbs: ∀h,G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈*[h] T →
57 ∀G2,L2,T2. ❪G1,L1,T❫ ⬂+ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
58 /3 width=5 by fpbs_fqup_trans, cpxs_fpbs/ qed.