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_transition/cpm_fpbc.ma".
16 include "basic_2/rt_computation/fpbg_fqus.ma".
17 include "basic_2/rt_computation/fpbg_cpxs.ma".
18 include "basic_2/rt_computation/cpms_fpbs.ma".
20 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
22 (* Forward lemmas with proper parallel rst-computation for closures *********)
24 lemma cpms_tneqx_fwd_fpbg (h) (n):
25 ∀G,L,T1,T2. ❨G,L❩ ⊢ T1 ➡*[h,n] T2 →
26 (T1 ≅ T2 → ⊥) → ❨G,L,T1❩ > ❨G,L,T2❩.
27 /3 width=3 by cpms_fwd_cpxs, cpxs_tneqx_fpbg/ qed-.
29 lemma fpbg_cpms_trans (h) (n):
30 ∀G1,G2,L1,L2,T1,T. ❨G1,L1,T1❩ > ❨G2,L2,T❩ →
31 ∀T2. ❨G2,L2❩ ⊢ T ➡*[h,n] T2 → ❨G1,L1,T1❩ > ❨G2,L2,T2❩.
32 /3 width=5 by fpbg_fpbs_trans, cpms_fwd_fpbs/ qed-.
34 lemma cpms_fpbg_trans (h) (n):
35 ∀G1,L1,T1,T. ❨G1,L1❩ ⊢ T1 ➡*[h,n] T →
36 ∀G2,L2,T2. ❨G1,L1,T❩ > ❨G2,L2,T2❩ → ❨G1,L1,T1❩ > ❨G2,L2,T2❩.
37 /3 width=5 by fpbs_fpbg_trans, cpms_fwd_fpbs/ qed-.
39 lemma fqup_cpms_fwd_fpbg (h):
40 ∀G1,G2,L1,L2,T1,T. ❨G1,L1,T1❩ ⬂+ ❨G2,L2,T❩ →
41 ∀n,T2. ❨G2,L2❩ ⊢ T ➡*[h,n] T2 → ❨G1,L1,T1❩ > ❨G2,L2,T2❩.
42 /3 width=5 by cpms_fwd_fpbs, fqup_fpbg, fpbg_fpbs_trans/ qed-.
44 lemma cpm_tneqx_cpm_cpms_teqx_sym_fwd_fpbg (h) (G) (L) (T1):
45 ∀n1,T. ❨G,L❩ ⊢ T1 ➡[h,n1] T → (T1 ≅ T → ⊥) →
46 ∀n2,T2. ❨G,L❩⊢ T ➡*[h,n2] T2 → T1 ≅ T2 → ❨G,L,T1❩ > ❨G,L,T1❩.
47 #h #G #L #T1 #n1 #T #H1T1 #H2T1 #n2 #T2 #H1T2 #H2T12
48 /4 width=10 by fpbc_fpbs_fpbg, cpms_fwd_fpbs, fpbs_teqg_trans, cpm_fwd_fpbc, teqx_sym/