]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/lambdadelta/basic_2/etc/fid/fle_fid.etc
update in delayed_updating
[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / fid / fle_fid.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/static/fid.ma".
16 include "basic_2/static/fle_fqup.ma".
17
18 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
19
20 (* Properties with free variables identity for restricted closures **********)
21
22 lemma fle_fid_sn: ∀L1,L2. |L1| = |L2| →
23                   ∀T1,T2. 𝐈⦃L1, T1⦄ → ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄.
24 #L1 #L2 #HL #T1 #T2 #HT1
25 elim (frees_total L1 T1) #f1 #Hf1
26 elim (frees_total L2 T2) #f2 #Hf2
27 /4 width=8 by lveq_length_eq, sle_isid_sn, ex4_4_intro/
28 qed.
29
30 (* Inversion lemmas with free variables identity for restricted closures ****)
31
32 lemma fle_inv_fid_dx: ∀L1,L2. |L1| = |L2| →
33                       ∀T1,T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →  𝐈⦃L2, T2⦄ → 𝐈⦃L1, T1⦄.
34 #L1 #L2 #HL #T1 #T2
35 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HL12 #Hf12 #HT2 #g1 #Hg1
36 elim (lveq_inj_length … HL12) // -HL -HL12 #H1 #H2 destruct
37 lapply (frees_mono … Hf1 … Hg1) -Hg1 #Hfg1
38 /4 width=5 by sle_inv_isid_dx, isid_eq_repl_back/
39 qed-.