]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/lambdadelta/basic_2/etc/referred/lfpxs.etc
update in delayed_updating
[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / referred / lfpxs.etc
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/notation/relations/predtysnstar_5.ma".
16 include "basic_2/i_static/tc_lfxs.ma".
17 include "basic_2/rt_transition/lfpx.ma".
18
19 (* UNBOUND PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ******)
20
21 definition lfpxs: ∀h. relation4 genv term lenv lenv ≝
22                   λh,G. tc_lfxs (cpx h G).
23
24 interpretation
25    "unbound parallel rt-computation on referred entries (local environment)"
26    'PRedTySnStar h T G L1 L2 = (lfpxs h G T L1 L2).
27
28 (* Basic properties *********************************************************)
29
30 (* Basic_2A1: was just: lpx_lpxs *)
31 lemma lfpx_lfpxs: ∀h,G,T,L1,L2. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
32 /2 width=1 by inj/ qed.
33
34 lemma lfpxs_step_dx: ∀h,G,T,L1,L,L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L → ⦃G, L⦄ ⊢ ⬈[h, T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
35 /2 width=3 by tc_lfxs_step_dx/ qed.
36
37 lemma lfpxs_step_sn: ∀h,G,T,L1,L,L2. ⦃G, L1⦄ ⊢ ⬈[h, T] L → ⦃G, L⦄ ⊢ ⬈*[h, T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
38 /2 width=3 by tc_lfxs_step_sn/ qed.
39
40 (* Basic inversion lemmas ***************************************************)
41
42 (* Basic_2A1: uses: lpxs_inv_atom1 *)
43 lemma lfpxs_inv_atom1: ∀h,I,G,L2. ⦃G, ⋆⦄ ⊢ ⬈*[h, ⓪{I}] L2 → L2 = ⋆.
44 /2 width=3 by tc_lfxs_inv_atom_sn/ qed-.
45
46 (* Basic_2A1: uses: lpxs_inv_atom2 *)
47 lemma lfpxs_inv_atom2: ∀h,I,G,L1. ⦃G, L1⦄ ⊢ ⬈*[h, ⓪{I}] ⋆ → L1 = ⋆.
48 /2 width=3 by tc_lfxs_inv_atom_dx/ qed-.
49
50 (* Basic forward lemmas *****************************************************)
51
52 lemma lfpxs_fwd_pair_sn: ∀h,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈*[h, ②{I}V.T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, V] L2.
53 /2 width=3 by tc_lfxs_fwd_pair_sn/ qed-.
54
55 lemma lfpxs_fwd_flat_dx: ∀h,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈*[h, ⓕ{I}V.T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
56 /2 width=3 by tc_lfxs_fwd_flat_dx/ qed-.