]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/lambdadelta/basic_2/etc/lpx_sn/lpr.etc
components: arity, csuba
[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / lpx_sn / lpr.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/predsn_3.ma".
16 include "basic_2/relocation/lpx_sn.ma".
17 include "basic_2/reduction/cpr.ma".
18
19 (* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************)
20
21 definition lpr: relation3 genv lenv lenv ≝ λG. lpx_sn (λ_.cpr G).
22
23 interpretation "parallel reduction (local environment, sn variant)"
24    'PRedSn G L1 L2 = (lpr G L1 L2).
25
26 (* Basic inversion lemmas ***************************************************)
27
28 (* Basic_1: includes: wcpr0_gen_sort *)
29 lemma lpr_inv_atom1: ∀G,L2. ⦃G, ⋆⦄ ⊢ ➡ L2 → L2 = ⋆.
30 /2 width=4 by lpx_sn_inv_atom1_aux/ qed-.
31
32 (* Basic_1: includes: wcpr0_gen_head *)
33 lemma lpr_inv_pair1: ∀I,G,K1,V1,L2. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ L2 →
34                      ∃∃K2,V2. ⦃G, K1⦄ ⊢ ➡ K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2 & L2 = K2.ⓑ{I}V2.
35 /2 width=3 by lpx_sn_inv_pair1_aux/ qed-.
36
37 lemma lpr_inv_atom2: ∀G,L1. ⦃G, L1⦄ ⊢ ➡ ⋆ → L1 = ⋆.
38 /2 width=4 by lpx_sn_inv_atom2_aux/ qed-.
39
40 lemma lpr_inv_pair2: ∀I,G,L1,K2,V2. ⦃G, L1⦄ ⊢ ➡ K2.ⓑ{I}V2 →
41                      ∃∃K1,V1. ⦃G, K1⦄ ⊢ ➡ K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2 & L1 = K1. ⓑ{I} V1.
42 /2 width=3 by lpx_sn_inv_pair2_aux/ qed-.
43
44 (* Basic properties *********************************************************)
45
46 (* Note: lemma 250 *)
47 lemma lpr_refl: ∀G,L. ⦃G, L⦄ ⊢ ➡ L.
48 /2 width=1 by lpx_sn_refl/ qed.
49
50 lemma lpr_pair: ∀I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ➡ K2 → ⦃G, K1⦄ ⊢ V1 ➡ V2 →
51                 ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ K2.ⓑ{I}V2.
52 /2 width=1 by lpx_sn_pair/ qed.
53
54 (* Basic forward lemmas *****************************************************)
55
56 lemma lpr_fwd_length: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → |L1| = |L2|.
57 /2 width=2 by lpx_sn_fwd_length/ qed-.
58
59 (* Basic_1: removed theorems 3: wcpr0_getl wcpr0_getl_back
60                                 pr0_subst1_back
61 *)