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 "basic_2/computation/fsb_aaa.ma".
16 include "basic_2/dynamic/snv_da_lpr.ma".
17 include "basic_2/dynamic/snv_lstas.ma".
18 include "basic_2/dynamic/snv_lstas_lpr.ma".
19 include "basic_2/dynamic/snv_lpr.ma".
21 (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
23 (* Main preservation properties *********************************************)
25 lemma snv_preserve: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] →
26 ∧∧ IH_da_cpr_lpr h g G L T
27 & IH_snv_cpr_lpr h g G L T
28 & IH_snv_lstas h g G L T
29 & IH_lstas_cpr_lpr h g G L T.
30 #h #g #G #L #T #HT elim (snv_fwd_aaa … HT) -HT
31 #A #HT @(aaa_ind_fpbg h g … HT) -G -L -T -A
32 #G #L #T #A #_ #IH -A @and4_intro
33 [ letin aux ≝ da_cpr_lpr_aux | letin aux ≝ snv_cpr_lpr_aux
34 | letin aux ≝ snv_lstas_aux | letin aux ≝ lstas_cpr_lpr_aux
36 @(aux … G L T) // #G0 #L0 #T0 #H elim (IH … H) -IH -H //
39 theorem da_cpr_lpr: ∀h,g,G,L,T. IH_da_cpr_lpr h g G L T.
40 #h #g #G #L #T #HT elim (snv_preserve … HT) /2 width=1 by/
43 theorem snv_cpr_lpr: ∀h,g,G,L,T. IH_snv_cpr_lpr h g G L T.
44 #h #g #G #L #T #HT elim (snv_preserve … HT) /2 width=1 by/
47 theorem snv_lstas: ∀h,g,G,L,T. IH_snv_lstas h g G L T.
48 #h #g #G #L #T #HT elim (snv_preserve … HT) /2 width=5 by/
51 theorem lstas_cpr_lpr: ∀h,g,G,L,T. IH_lstas_cpr_lpr h g G L T.
52 #h #g #G #L #T #HT elim (snv_preserve … HT) /2 width=3 by/
55 (* Advanced preservation properties *****************************************)