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 *)
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15 include "basic_2/notation/relations/predsnstar_4.ma".
16 include "basic_2/relocation/lex.ma".
17 include "basic_2/rt_computation/cprs_ext.ma".
19 (* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
21 definition lprs (h) (G): relation lenv ≝
22 lex (λL.cpms h G L 0).
25 "parallel r-computation on all entries (local environment)"
26 'PRedSnStar h G L1 L2 = (lprs h G L1 L2).
28 (* Basic properties *********************************************************)
30 lemma lprs_refl (h) (G): ∀L. ⦃G, L⦄ ⊢ ➡*[h] L.
31 /2 width=1 by lex_refl/ qed.
33 (* Basic_2A1: uses: lprs_pair_refl *)
34 lemma lprs_bind_refl_dx (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡*[h] L2 →
35 ∀I. ⦃G, L1.ⓘ{I}⦄ ⊢ ➡*[h] L2.ⓘ{I}.
36 /2 width=1 by lex_bind_refl_dx/ qed.
38 (* Basic inversion lemmas ***************************************************)
40 (* Basic_2A1: uses: lprs_inv_atom1 *)
41 lemma lprs_inv_atom_sn (h) (G): ∀L2. ⦃G, ⋆⦄ ⊢ ➡*[h] L2 → L2 = ⋆.
42 /2 width=2 by lex_inv_atom_sn/ qed-.
44 (* Basic_2A1: uses: lprs_inv_atom2 *)
45 lemma lprs_inv_atom_dx (h) (G): ∀L1. ⦃G, L1⦄ ⊢ ➡*[h] ⋆ → L1 = ⋆.
46 /2 width=2 by lex_inv_atom_dx/ qed-.