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_proper.ma".
24 include "delayed_updating/substitution/lift_prototerm_eq.ma".
26 include "delayed_updating/syntax/path_head_structure.ma".
27 include "delayed_updating/syntax/path_structure_depth.ma".
28 include "delayed_updating/syntax/path_structure_reverse.ma".
29 include "delayed_updating/syntax/path_depth_reverse.ma".
31 (* IMMEDIATE FOCUSED REDUCTION **********************************************)
33 (* Constructions with unwind ************************************************)
35 lemma ifr_unwind_bi (f) (p) (q) (t1) (t2):
36 t1 Ļµ š ā t1ā(pāš¦) Ļµ š ā
37 t1 ā”š¢š[p,q] t2 ā ā¼[f]t1 ā”š¢š[āp,āq] ā¼[f]t2.
38 #f #p #q #t1 #t2 #H1t1 #H2t1
40 @(ex_intro ā¦ (āāq)) @and3_intro
41 [ -H1t1 -H2t1 -Ht1 -Ht2
42 >structure_L_sn >structure_reverse
43 >H1n in ā¢ (??%?); >path_head_structure_depth <H1n -H1n //
44 | lapply (in_comp_unwind2_path_term f ā¦ Ht1) -Ht2 -Ht1 -H1t1 -H2t1
45 <unwind2_path_d_dx >(list_append_rcons_sn ā¦ p) <reverse_append
46 lapply (unwind2_rmap_append_pap_closed f ā¦ (pāš)į“æ ā¦ H1n) -H1n
47 <reverse_lcons <depth_L_dx #H2n
48 lapply (eq_inv_ninj_bi ā¦ H2n) -H2n #H2n <H2n -H2n #Ht1 //
49 | lapply (unwind2_term_eq_repl_dx f ā¦ Ht2) -Ht2 #Ht2
50 @(subset_eq_trans ā¦ Ht2) -t2
51 @(subset_eq_trans ā¦ (unwind2_term_fsubst ā¦))
52 [ @fsubst_eq_repl [ // | // ]
53 @(subset_eq_canc_sn ā¦ (lift_term_eq_repl_dx ā¦))
54 [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
55 @(subset_eq_trans ā¦ (lift_unwind2_term_after ā¦))
56 @(subset_eq_canc_dx ā¦ (unwind2_term_after_lift ā¦))
57 @unwind2_term_eq_repl_sn
58 (* Note: crux of the proof begins *)
59 >list_append_rcons_sn <reverse_append
60 @(stream_eq_trans ā¦ (tr_compose_uni_dx ā¦))
62 [ <unwind2_rmap_append_pap_closed //
63 | >unwind2_rmap_A_sn <reverse_rcons
64 /2 width=1 by tls_unwind2_rmap_closed/
66 (* Note: crux of the proof ends *)
68 | /2 width=2 by ex_intro/
69 | /2 width=6 by lift_term_proper/