]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/lambdadelta/static_2/static/reqg_fqup.ma
update in ground and delayed updating
[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / reqg_fqup.ma
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 "static_2/static/rex_fqup.ma".
16 include "static_2/static/reqg.ma".
17
18 (* GEBERIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ***********)
19
20 (* Advanced properties ******************************************************)
21
22 lemma reqg_refl (S):
23       reflexive … S →
24       c_reflexive … (reqg S).
25 /3 width=1 by rex_refl, teqg_refl/ qed.
26
27 lemma reqg_pair_refl (S):
28       reflexive … S →
29       ∀V1,V2. V1 ≛[S] V2 →
30       ∀I,L. ∀T:term. L.ⓑ[I]V1 ≛[S,T] L.ⓑ[I]V2.
31 /3 width=1 by rex_pair_refl, teqg_refl/ qed.
32
33 (* Advanced inversion lemmas ************************************************)
34
35 lemma reqg_inv_bind_void (S):
36       ∀p,I,L1,L2,V,T. L1 ≛[S,ⓑ[p,I]V.T] L2 →
37       ∧∧ L1 ≛[S,V] L2 & L1.ⓧ ≛[S,T] L2.ⓧ.
38 /2 width=3 by rex_inv_bind_void/ qed-.
39
40 (* Advanced forward lemmas **************************************************)
41
42 lemma reqg_fwd_bind_dx_void (S):
43       ∀p,I,L1,L2,V,T.
44       L1 ≛[S,ⓑ[p,I]V.T] L2 → L1.ⓧ ≛[S,T] L2.ⓧ.
45 /2 width=4 by rex_fwd_bind_dx_void/ qed-.