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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_tdeq.ma".
16 include "static_2/static/rex_length.ma".
17 include "static_2/static/rex_fsle.ma".
18 include "static_2/static/rdeq.ma".
19
20 (* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
21
22 (* Advanved properties with free variables inclusion ************************)
23
24 lemma rdeq_fsge_comp (h) (o): rex_fsge_compatible (cdeq h o).
25 #h #o #L1 #L2 #T * #f1 #Hf1 #HL12
26 lapply (frees_rdeq_conf h o … Hf1 … HL12)
27 lapply (sex_fwd_length … HL12)
28 /3 width=8 by lveq_length_eq, ex4_4_intro/ (**) (* full auto fails *)
29 qed-.
30
31 (* Properties with length for local environments ****************************)
32
33 (* Basic_2A1: uses: lleq_sort *)
34 lemma rdeq_sort_length (h) (o): ∀L1,L2. |L1| = |L2| → ∀s. L1 ≛[h, o, ⋆s] L2.
35 /2 width=1 by rex_sort_length/ qed.
36
37 (* Basic_2A1: uses: lleq_gref *)
38 lemma rdeq_gref_length (h) (o): ∀L1,L2. |L1| = |L2| → ∀l. L1 ≛[h, o, §l] L2.
39 /2 width=1 by rex_gref_length/ qed.
40
41 lemma rdeq_unit_length (h) (o): ∀L1,L2. |L1| = |L2| →
42                                 ∀I. L1.ⓤ{I} ≛[h, o, #0] L2.ⓤ{I}.
43 /2 width=1 by rex_unit_length/ qed.
44
45 (* Basic_2A1: uses: lleq_lift_le lleq_lift_ge *)
46 lemma rdeq_lifts_bi (h) (o): ∀L1,L2. |L1| = |L2| → ∀K1,K2,T. K1 ≛[h, o, T] K2 →
47                              ∀b,f. ⬇*[b, f] L1 ≘ K1 → ⬇*[b, f] L2 ≘ K2 →
48                              ∀U. ⬆*[f] T ≘ U → L1 ≛[h, o, U] L2.
49 /3 width=9 by rex_lifts_bi, tdeq_lifts_sn/ qed-.
50
51 (* Forward lemmas with length for local environments ************************)
52
53 (* Basic_2A1: lleq_fwd_length *)
54 lemma rdeq_fwd_length (h) (o): ∀L1,L2. ∀T:term. L1 ≛[h, o, T] L2 → |L1| = |L2|.
55 /2 width=3 by rex_fwd_length/ qed-.