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 "static_2/relocation/lex_tc.ma".
16 include "basic_2/rt_computation/cpxs_lpx.ma".
17 include "basic_2/rt_computation/lpxs.ma".
19 (* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
21 (* Properties with unbound rt-transition for full local environments ********)
23 lemma lpx_lpxs (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ⬈[h] L2 → ❪G,L1❫ ⊢ ⬈*[h] L2.
24 /3 width=3 by lpx_cpxs_trans, lex_CTC_inj/ qed.
26 (* Basic_2A1: was: lpxs_strap2 *)
27 lemma lpxs_step_sn (h) (G): ∀L1,L. ❪G,L1❫ ⊢ ⬈[h] L →
28 ∀L2. ❪G,L❫ ⊢ ⬈*[h] L2 → ❪G,L1❫ ⊢ ⬈*[h] L2.
29 /3 width=3 by lpx_cpxs_trans, lex_CTC_step_sn/ qed-.
31 (* Basic_2A1: was: lpxs_strap1 *)
32 lemma lpxs_step_dx (h) (G): ∀L1,L. ❪G,L1❫ ⊢ ⬈*[h] L →
33 ∀L2. ❪G,L❫ ⊢ ⬈[h] L2 → ❪G,L1❫ ⊢ ⬈*[h] L2.
34 /3 width=3 by lpx_cpxs_trans, lex_CTC_step_dx/ qed-.
36 (* Eliminators with unbound rt-transition for full local environments *******)
38 (* Basic_2A1: was: lpxs_ind_dx *)
39 lemma lpxs_ind_sn (h) (G) (L2): ∀Q:predicate lenv. Q L2 →
40 (∀L1,L. ❪G,L1❫ ⊢ ⬈[h] L → ❪G,L❫ ⊢ ⬈*[h] L2 → Q L → Q L1) →
41 ∀L1. ❪G,L1❫ ⊢ ⬈*[h] L2 → Q L1.
42 /3 width=7 by lpx_cpxs_trans, cpx_refl, lex_CTC_ind_sn/ qed-.
44 (* Basic_2A1: was: lpxs_ind *)
45 lemma lpxs_ind_dx (h) (G) (L1): ∀Q:predicate lenv. Q L1 →
46 (∀L,L2. ❪G,L1❫ ⊢ ⬈*[h] L → ❪G,L❫ ⊢ ⬈[h] L2 → Q L → Q L2) →
47 ∀L2. ❪G,L1❫ ⊢ ⬈*[h] L2 → Q L2.
48 /3 width=7 by lpx_cpxs_trans, cpx_refl, lex_CTC_ind_dx/ qed-.
50 (* Properties with context-sensitive extended rt-transition for terms *******)
52 lemma lpxs_cpx_trans (h) (G): s_r_transitive … (cpx h G) (λ_.lpxs h G).
53 #h #G #L2 #T1 #T2 #HT12 #L1 #HL12
54 @(s_r_trans_CTC2 ???????? HT12) -HT12
55 /2 width=4 by lpx_cpxs_trans, lex_inv_CTC/
58 (* Properties with context-sensitive extended rt-computation for terms ******)
60 (* Note: alternative proof by s_r_to_s_rs_trans *)
61 lemma lpxs_cpxs_trans (h) (G): s_rs_transitive … (cpx h G) (λ_.lpxs h G).
62 #h #G @s_r_trans_CTC1 /2 width=3 by lpxs_cpx_trans/
65 (* Advanced properties ******************************************************)
67 (* Basic_2A1: was: lpxs_pair2 *)
68 lemma lpxs_pair_dx (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ⬈*[h] L2 →
69 ∀V1,V2. ❪G,L2❫ ⊢ V1 ⬈*[h] V2 →
70 ∀I. ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈*[h] L2.ⓑ[I]V2.
71 /3 width=3 by lpxs_pair, lpxs_cpxs_trans/ qed.