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/syntax/lveq_length.ma".
16 include "basic_2/relocation/lifts_tdeq.ma".
17 include "basic_2/static/lfxs_length.ma".
18 include "basic_2/static/lfdeq.ma".
20 (* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
22 (* Advanved properties ******************************************************)
24 lemma lfdeq_fle_comp: ∀h,o. lfxs_fle_compatible (cdeq h o).
25 #h #o #L1 #L2 #T * #f1 #Hf1 #HL12
26 lapply (frees_lfdeq_conf h o … Hf1 … HL12)
27 lapply (lexs_fwd_length … HL12)
28 /3 width=8 by lveq_length_eq, ex4_4_intro/ (**) (* full auto fails *)
31 (* Properties with length for local environments ****************************)
33 (* Basic_2A1: uses: lleq_lift_le lleq_lift_ge *)
34 lemma lfdeq_lifts_bi: ∀L1,L2. |L1| = |L2| → ∀h,o,K1,K2,T. K1 ≛[h, o, T] K2 →
35 ∀b,f. ⬇*[b, f] L1 ≡ K1 → ⬇*[b, f] L2 ≡ K2 →
36 ∀U. ⬆*[f] T ≡ U → L1 ≛[h, o, U] L2.
37 /3 width=9 by lfxs_lifts_bi, tdeq_lifts_sn/ qed-.
39 (* Forward lemmas with length for local environments ************************)
41 (* Basic_2A1: lleq_fwd_length *)
42 lemma lfdeq_fwd_length: ∀h,o,L1,L2. ∀T:term. L1 ≛[h, o, T] L2 → |L1| = |L2|.
43 /2 width=3 by lfxs_fwd_length/ qed-.