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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 include "basic_2/rt_computation/cprs_ctc.ma".
16 include "basic_2/rt_computation/lprs.ma".
17
18 (* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
19
20 (* Properties with contextual transitive closure ****************************)
21
22 lemma lprs_CTC (h) (G):
23                ∀L1,L2. L1⪤[CTC … (λL. cpm h G L 0)] L2 → ⦃G,L1⦄⊢ ➡*[h] L2.
24 /3 width=3 by cprs_CTC, lex_co/ qed.
25
26 (* Inversion lemmas with contextual transitive closure **********************)
27
28 lemma lprs_inv_CTC (h) (G):
29                    ∀L1,L2. ⦃G,L1⦄⊢ ➡*[h] L2 → L1⪤[CTC … (λL. cpm h G L 0)] L2.
30 /3 width=3 by cprs_inv_CTC, lex_co/ qed-.