]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
basic_2: stronger supclosure allows better inversion lemmas
[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lfxs_lfxs.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 "basic_2/relocation/lexs_lexs.ma".
16 include "basic_2/static/lfxs.ma".
17
18 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
19
20 (* Main properties **********************************************************)
21
22 theorem lfxs_bind: ∀R,p,I,L1,L2,V1,V2,T.
23                    L1 ⦻*[R, V1] L2 → L1.ⓑ{I}V1 ⦻*[R, T] L2.ⓑ{I}V2 →
24                    L1 ⦻*[R, ⓑ{p,I}V1.T] L2.
25 #R #p #I #L1 #L2 #V1 #V2 #T * #f1 #HV #Hf1 * #f2 #HT #Hf2
26 elim (lexs_fwd_pair … Hf2) -Hf2 #Hf2 #_ elim (sor_isfin_ex f1 (⫱f2))
27 /3 width=7 by frees_fwd_isfin, frees_bind, lexs_join, isfin_tl, ex2_intro/
28 qed.
29
30 theorem lfxs_flat: ∀R,I,L1,L2,V,T.
31                    L1 ⦻*[R, V] L2 → L1 ⦻*[R, T] L2 →
32                    L1 ⦻*[R, ⓕ{I}V.T] L2.
33 #R #I #L1 #L2 #V #T * #f1 #HV #Hf1 * #f2 #HT #Hf2 elim (sor_isfin_ex f1 f2)
34 /3 width=7 by frees_fwd_isfin, frees_flat, lexs_join, ex2_intro/
35 qed.