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/ifr.ma".
17 include "delayed_updating/substitution/fsubst_lift.ma".
18 include "delayed_updating/substitution/fsubst_eq.ma".
19 include "delayed_updating/substitution/lift_path_head.ma".
20 include "delayed_updating/substitution/lift_rmap_head.ma".
22 include "ground/relocation/tr_uni_compose.ma".
23 include "ground/relocation/tr_compose_eq.ma".
25 (* IMMEDIATE FOCUSED REDUCTION **********************************************)
27 (* Constructions with lift **************************************************)
29 theorem ifr_lift_bi (f) (p) (q) (t1) (t2):
30 t1 ā”š¢š[p,q] t2 ā ā[f]t1 ā”š¢š[ā[f]p,ā[ā[pāšāš]f]q] ā[f]t2.
33 @(ex_intro ā¦ ((ā[pāšāšāq]f)ļ¼ ā§£āØnā©)) @and3_intro
35 <lift_rmap_L_dx >lift_path_L_sn
36 <(lift_path_head ā¦ H1n) in ā¢ (??%?); -H1n //
37 | lapply (in_comp_lift_path_term f ā¦ Ht1) -Ht2 -Ht1 -H1n
38 <lift_path_d_dx #Ht1 //
39 | lapply (lift_term_eq_repl_dx f ā¦ Ht2) -Ht2 #Ht2 -Ht1
40 @(subset_eq_trans ā¦ Ht2) -t2
41 @(subset_eq_trans ā¦ (lift_term_fsubst ā¦))
42 @fsubst_eq_repl [ // | <lift_path_append // ]
43 @(subset_eq_canc_sn ā¦ (lift_term_eq_repl_dx ā¦))
44 [ @lift_term_grafted_S | skip ]
45 @(subset_eq_trans ā¦ (lift_term_after ā¦))
46 @(subset_eq_canc_dx ā¦ (lift_term_after ā¦))
48 (* Note: crux of the proof begins *)
49 @(stream_eq_trans ā¦ (tr_compose_uni_dx ā¦))
50 @tr_compose_eq_repl //
51 >list_append_rcons_sn in H1n; #H1n >lift_rmap_A_dx
52 /2 width=1 by tls_lift_rmap_closed/
53 (* Note: crux of the proof ends *)