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/lexs_length.ma".
16 include "basic_2/static/lfxs_drops.ma".
18 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
20 (* Forward lemmas with length for local environments ************************)
22 (* Basic_2A1: uses: llpx_sn_fwd_length *)
23 lemma lfxs_fwd_length: ∀R,L1,L2,T. L1 ⪤*[R, T] L2 → |L1| = |L2|.
24 #R #L1 #L2 #T * /2 width=4 by lexs_fwd_length/
27 (* Properties with length for local environments ****************************)
29 (* Basic_2A1: uses: llpx_sn_lift_le llpx_sn_lift_ge *)
30 lemma lfxs_lifts_bi: ∀R.d_liftable2_sn … lifts R →
31 ∀L1,L2. |L1| = |L2| → ∀K1,K2,T. K1 ⪤*[R, T] K2 →
32 ∀b,f. ⬇*[b, f] L1 ≡ K1 → ⬇*[b, f] L2 ≡ K2 →
33 ∀U. ⬆*[f] T ≡ U → L1 ⪤*[R, U] L2.
34 #R #HR #L1 #L2 #HL12 #K1 #K2 #T * #f1 #Hf1 #HK12 #b #f #HLK1 #HLK2 #U #HTU
35 elim (frees_total L1 U) #f2 #Hf2
36 lapply (frees_fwd_coafter … Hf2 … HLK1 … HTU … Hf1) -HTU #Hf
37 /4 width=12 by lexs_length_cfull, lexs_liftable_co_dedropable_bi, cext2_d_liftable2_sn, cfull_lift_sn, ex2_intro/