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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/relocation/lifts_teqg.ma".
16 include "static_2/static/rex_length.ma".
17 include "static_2/static/rex_fsle.ma".
18 include "static_2/static/reqg.ma".
19
20 (* GENERIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ***********)
21
22 (* Advanced properties with free variables inclusion ************************)
23
24 lemma reqg_fsge_comp (S):
25       reflexive … S →
26       rex_fsge_compatible (ceqg S).
27 #S #HS #L1 #L2 #T * #f1 #Hf1 #HL12
28 lapply (frees_seqg_conf … Hf1 … HL12)
29 lapply (sex_fwd_length … HL12)
30 /3 width=8 by lveq_length_eq, ex4_4_intro/ (**) (* full auto fails *)
31 qed-.
32
33 (* Properties with length for local environments ****************************)
34
35 (* Basic_2A1: uses: lleq_sort *)
36 lemma reqg_sort_length (S):
37       ∀L1,L2. |L1| = |L2| → ∀s. L1 ≛[S,⋆s] L2.
38 /2 width=1 by rex_sort_length/ qed.
39
40 (* Basic_2A1: uses: lleq_gref *)
41 lemma reqg_gref_length (S):
42       ∀L1,L2. |L1| = |L2| → ∀l. L1 ≛[S,§l] L2.
43 /2 width=1 by rex_gref_length/ qed.
44
45 lemma reqg_unit_length (S):
46       ∀L1,L2. |L1| = |L2| →
47       ∀I. L1.ⓤ[I] ≛[S,#0] L2.ⓤ[I].
48 /2 width=1 by rex_unit_length/ qed.
49
50 (* Basic_2A1: uses: lleq_lift_le lleq_lift_ge *)
51 lemma reqg_lifts_bi (S):
52       ∀L1,L2. |L1| = |L2| → ∀K1,K2,T. K1 ≛[S,T] K2 →
53       ∀b,f. ⇩*[b,f] L1 ≘ K1 → ⇩*[b,f] L2 ≘ K2 →
54       ∀U. ⇧*[f] T ≘ U → L1 ≛[S,U] L2.
55 /3 width=9 by rex_lifts_bi, teqg_lifts_sn/ qed-.
56
57 (* Forward lemmas with length for local environments ************************)
58
59 (* Basic_2A1: lleq_fwd_length *)
60 lemma reqg_fwd_length (S):
61       ∀L1,L2. ∀T:term. L1 ≛[S,T] L2 → |L1| = |L2|.
62 /2 width=3 by rex_fwd_length/ qed-.