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/lprs_ctc.ma".
17 include "basic_2/rt_computation/cprs_lpr.ma".
19 (* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
21 (* Properties with transitive closure ***************************************)
23 lemma lprs_TC (h) (G):
24 ∀L1,L2. TC … (lex (λL.cpm h G L 0)) L1 L2 → ❪G,L1❫⊢ ➡*[h,0] L2.
25 /4 width=3 by lprs_CTC, lex_CTC, lpr_cprs_trans/ qed.
27 (* Inversion lemmas with transitive closure *********************************)
29 lemma lprs_inv_TC (h) (G):
30 ∀L1,L2. ❪G,L1❫⊢ ➡*[h,0] L2 → TC … (lex (λL.cpm h G L 0)) L1 L2.
31 /3 width=3 by lprs_inv_CTC, lex_inv_CTC/ qed-.