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/fsubst_eq.ma".
19 include "delayed_updating/substitution/lift_constructors.ma".
20 include "delayed_updating/substitution/lift_preterm_eq.ma".
21 include "delayed_updating/substitution/lift_structure_depth.ma".
22 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
23 include "delayed_updating/syntax/path_structure_depth.ma".
24 include "ground/relocation/tr_uni_compose.ma".
25 include "ground/relocation/tr_pap_pushs.ma".
27 include "ground/lib/stream_eq_eq.ma".
29 (* DELAYED FOCUSED REDUCTION ************************************************)
31 lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
32 t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[⊗p,⊗q] ↑[f]t2.
33 #f #p #q #t1 #t2 #H0t1
34 * #b #n * #Hb #Hn #Ht1 #Ht2
35 @(ex1_2_intro … (⊗b) (↑❘⊗q❘)) @and4_intro
37 | #g <lift_rmap_structure <depth_structure
38 >tr_pushs_swap <tr_pap_pushs_le //
39 | lapply (in_comp_lift_bi f … Ht1) -Ht1 -H0t1 -Hb -Ht2
40 <lift_path_d_empty_dx //
41 | lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
42 @(subset_eq_trans … Ht2) -t2
43 @(subset_eq_trans … (lift_fsubst …))
44 [ <lift_rmap_append <lift_rmap_A_sn <lift_rmap_append <lift_rmap_L_sn
45 <structure_append <structure_A_sn <structure_append <structure_L_sn
46 <depth_append <depth_L_sn <depth_structure <depth_structure
47 @fsubst_eq_repl [ // ]
48 @(subset_eq_trans … (lift_iref …))
49 @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
50 [ @lift_grafted_S /2 width=2 by ex_intro/ | skip ]
51 @(subset_eq_trans … (lift_term_after …))
52 @(subset_eq_canc_dx … (lift_term_after …))
53 @lift_term_eq_repl_sn -t1
54 @(stream_eq_trans … (tr_compose_uni_dx …))
56 >nrplus_inj_dx <tr_pap_plus
59 | /2 width=2 by ex_intro/