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/relocation/lifts_tdeq.ma".
16 include "basic_2/static/lfxs_drops.ma".
17 include "basic_2/static/lfdeq.ma".
19 (* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
21 (* Properties with generic slicing for local environments *******************)
23 lemma lfdeq_lifts_sn: ∀h,o. f_dedropable_sn (cdeq h o).
24 /3 width=5 by lfxs_liftable_dedropable_sn, tdeq_lifts_sn/ qed-.
26 (* Inversion lemmas with generic slicing for local environments *************)
28 lemma lfdeq_inv_lifts_sn: ∀h,o. f_dropable_sn (cdeq h o).
29 /2 width=5 by lfxs_dropable_sn/ qed-.
31 (* Note: missing in basic_2A1 *)
32 lemma lfdeq_inv_lifts_dx: ∀h,o. f_dropable_dx (cdeq h o).
33 /2 width=5 by lfxs_dropable_dx/ qed-.
35 (* Basic_2A1: uses: lleq_inv_lift_le lleq_inv_lift_be lleq_inv_lift_ge *)
36 lemma lfdeq_inv_lifts_bi: ∀h,o,L1,L2,U. L1 ≛[h, o, U] L2 → ∀b,f. 𝐔⦃f⦄ →
37 ∀K1,K2. ⬇*[b, f] L1 ≘ K1 → ⬇*[b, f] L2 ≘ K2 →
38 ∀T. ⬆*[f] T ≘ U → K1 ≛[h, o, T] K2.
39 /2 width=10 by lfxs_inv_lifts_bi/ qed-.
41 lemma lfdeq_inv_lref_pair_sn: ∀h,o,L1,L2,i. L1 ≛[h, o, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 →
42 ∃∃K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
43 /2 width=3 by lfxs_inv_lref_pair_sn/ qed-.
45 lemma lfdeq_inv_lref_pair_dx: ∀h,o,L1,L2,i. L1 ≛[h, o, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 →
46 ∃∃K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
47 /2 width=3 by lfxs_inv_lref_pair_dx/ qed-.