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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 *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "static_2/s_computation/fqus_fqup.ma".
16 include "static_2/static/feqx_fqup.ma".
17 include "basic_2/rt_computation/fpbs_fqus.ma".
19 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
21 (* Advanced properties ******************************************************)
23 lemma teqx_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 feqx_fpbs_trans, teqx_feqx/ qed-.
27 lemma fpbs_teqx_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_feqx_trans, teqx_feqx/ 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-.