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/unwind/unwind2_preterm_fsubst.ma".
18 include "delayed_updating/unwind/unwind2_preterm_eq.ma".
19 include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
20 include "delayed_updating/unwind/unwind2_rmap_head.ma".
22 include "delayed_updating/substitution/fsubst_eq.ma".
23 include "delayed_updating/substitution/lift_prototerm_eq.ma".
25 include "delayed_updating/syntax/path_head_structure.ma".
26 include "delayed_updating/syntax/path_structure_depth.ma".
28 (* IMMEDIATE FOCUSED REDUCTION **********************************************)
30 (* Constructions with unwind2 ***********************************************)
32 lemma ifr_unwind_bi (f) (t1) (t2) (r):
33 t1 Ļµ š ā r Ļµ š ā
34 t1 ā”š¢š[r] t2 ā ā¼[f]t1 ā”š¢š[ār] ā¼[f]t2.
35 #f #t1 #t2 #r #H1t1 #H2r
36 * #p #q #k #Hr #H1k #Ht1 #Ht2 destruct
37 @(ex4_3_intro ā¦ (āp) (āq) (āāq))
38 [ -H1t1 -H2r -H1k -Ht1 -Ht2 //
39 | -H1t1 -H2r -Ht1 -Ht2
41 >H1k in ā¢ (??%?); >path_head_structure_depth <H1k -H1k //
42 | lapply (in_comp_unwind2_path_term f ā¦ Ht1) -Ht2 -Ht1 -H1t1 -H2r
43 <unwind2_path_d_dx <list_append_rcons_sn
44 lapply (unwind2_rmap_append_pap_closed f ā¦ (pāš) ā¦ H1k) -H1k
46 lapply (eq_inv_ninj_bi ā¦ H2k) -H2k #H2k <H2k -H2k #Ht1 //
47 | lapply (unwind2_term_eq_repl_dx f ā¦ Ht2) -Ht2 #Ht2
48 @(subset_eq_trans ā¦ Ht2) -t2
49 @(subset_eq_trans ā¦ (unwind2_term_fsubst_pic ā¦))
50 [ @fsubst_eq_repl [ // | // ]
51 @(subset_eq_canc_sn ā¦ (lift_term_eq_repl_dx ā¦))
52 [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
53 @(subset_eq_trans ā¦ (lift_unwind2_term_after ā¦))
54 @(subset_eq_canc_dx ā¦ (unwind2_lift_term_after ā¦))
55 @unwind2_term_eq_repl_sn
56 (* Note: crux of the proof begins *)
58 @(stream_eq_trans ā¦ (tr_compose_uni_dx ā¦))
60 [ <unwind2_rmap_append_pap_closed //
62 /2 width=1 by tls_unwind2_rmap_closed/
64 (* Note: crux of the proof ends *)
66 | /2 width=2 by ex_intro/