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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/relocation/lex_tc.ma".
16 include "basic_2/rt_computation/cpxs_lpx.ma".
17 include "basic_2/rt_computation/lpxs.ma".
19 (* EXTENDED PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS *************)
21 (* Properties with extended rt-transition for full local environments *******)
24 ∀L1,L2. ❨G,L1❩ ⊢ ⬈ L2 → ❨G,L1❩ ⊢ ⬈* L2.
25 /3 width=3 by lpx_cpxs_trans, lex_CTC_inj/ qed.
27 (* Basic_2A1: was: lpxs_strap2 *)
28 lemma lpxs_step_sn (G):
30 ∀L2. ❨G,L❩ ⊢ ⬈* L2 → ❨G,L1❩ ⊢ ⬈* L2.
31 /3 width=3 by lpx_cpxs_trans, lex_CTC_step_sn/ qed-.
33 (* Basic_2A1: was: lpxs_strap1 *)
34 lemma lpxs_step_dx (G):
35 ∀L1,L. ❨G,L1❩ ⊢ ⬈* L →
36 ∀L2. ❨G,L❩ ⊢ ⬈ L2 → ❨G,L1❩ ⊢ ⬈* L2.
37 /3 width=3 by lpx_cpxs_trans, lex_CTC_step_dx/ qed-.
39 (* Eliminators with extended rt-transition for full local environments ******)
41 (* Basic_2A1: was: lpxs_ind_dx *)
42 lemma lpxs_ind_sn (G) (L2) (Q:predicate …):
44 (∀L1,L. ❨G,L1❩ ⊢ ⬈ L → ❨G,L❩ ⊢ ⬈* L2 → Q L → Q L1) →
45 ∀L1. ❨G,L1❩ ⊢ ⬈* L2 → Q L1.
46 /3 width=7 by lpx_cpxs_trans, cpx_refl, lex_CTC_ind_sn/ qed-.
48 (* Basic_2A1: was: lpxs_ind *)
49 lemma lpxs_ind_dx (G) (L1) (Q:predicate …):
51 (∀L,L2. ❨G,L1❩ ⊢ ⬈* L → ❨G,L❩ ⊢ ⬈ L2 → Q L → Q L2) →
52 ∀L2. ❨G,L1❩ ⊢ ⬈* L2 → Q L2.
53 /3 width=7 by lpx_cpxs_trans, cpx_refl, lex_CTC_ind_dx/ qed-.
55 (* Properties with context-sensitive extended rt-transition for terms *******)
57 lemma lpxs_cpx_trans (G):
58 s_r_transitive … (cpx G) (λ_.lpxs G).
59 #G #L2 #T1 #T2 #HT12 #L1 #HL12
60 @(s_r_trans_CTC2 ???????? HT12) -HT12
61 /2 width=4 by lpx_cpxs_trans, lex_inv_CTC/
64 (* Properties with context-sensitive extended rt-computation for terms ******)
66 (* Note: alternative proof by s_r_to_s_rs_trans *)
67 lemma lpxs_cpxs_trans (G):
68 s_rs_transitive … (cpx G) (λ_.lpxs G).
69 #G @s_r_trans_CTC1 /2 width=3 by lpxs_cpx_trans/
72 (* Advanced properties ******************************************************)
74 (* Basic_2A1: was: lpxs_pair2 *)
75 lemma lpxs_pair_dx (G):
76 ∀L1,L2. ❨G,L1❩ ⊢ ⬈* L2 →
77 ∀V1,V2. ❨G,L2❩ ⊢ V1 ⬈* V2 →
78 ∀I. ❨G,L1.ⓑ[I]V1❩ ⊢ ⬈* L2.ⓑ[I]V2.
79 /3 width=3 by lpxs_pair, lpxs_cpxs_trans/ qed.