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 "delayed_updating/reduction/dfr.ma".
16 include "delayed_updating/reduction/ifr.ma".
17 include "delayed_updating/substitution/fsubst_lift.ma".
18 include "delayed_updating/substitution/lift_structure_depth.ma".
19 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
20 include "delayed_updating/syntax/path_structure_depth.ma".
21 include "ground/relocation/tr_id_pap.ma".
22 include "ground/relocation/tr_id_pushs.ma".
24 (* DELAYED FOCUSED REDUCTION ************************************************)
26 lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
27 t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[⊗p,⊗q] ↑[f]t2.
28 #f #p #q #t1 #t2 #H0t1
29 * #b #n * #Hb #Hn #Ht1 #Ht2
30 @(ex1_2_intro … (⊗b) (❘⊗q❘)) @and4_intro
33 | lapply (in_comp_lift_bi f … Ht1) -Ht1 -H0t1 -Hb -Ht2 #Ht1
35 | lapply (eq_lift_bi f … Ht2) -Ht2 #Ht2
36 @(subset_eq_trans … Ht2) -t2
37 @(subset_eq_trans … (lift_fsubst …))
38 [ <structure_append <structure_A_sn <structure_append <structure_L_sn
40 | /2 width=2 by ex_intro/