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 *)
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15 include "delayed_updating/reduction/ifr.ma".
17 include "delayed_updating/unwind/unwind2_constructors.ma".
18 include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
19 include "delayed_updating/unwind/unwind2_preterm_eq.ma".
20 include "delayed_updating/unwind/unwind2_prototerm_inner.ma".
21 include "delayed_updating/unwind/unwind2_rmap_head.ma".
23 include "delayed_updating/substitution/fsubst_eq.ma".
25 include "delayed_updating/syntax/prototerm_proper_inner.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 Ο΅ π β t1β(pβπ¦) β§Έβ¬ π β
37 t1 β‘π’π[p,q] t2 β βΌ[f]t1 β‘π’π[βp,βq] βΌ[f]t2.
38 #f #p #q #t1 #t2 #H1t1 #H2t1
40 @(ex_intro β¦ (ββq)) @and3_intro
41 [ -H1t1 -H2t1 -Ht1 -Ht2
42 >structure_L_sn >structure_reverse
43 >H1n >path_head_structure_depth <H1n -H1n //
44 | lapply (in_comp_unwind2_path_term f β¦ Ht1) -Ht2 -Ht1 -H1t1 -H2t1
46 >list_append_rcons_sn in H1n; <reverse_append #H1n
47 lapply (unwind2_rmap_append_pap_closed f β¦ H1n)
48 <reverse_lcons <depth_L_dx #H2n
49 lapply (eq_inv_ninj_bi β¦ H2n) -H2n #H2n <H2n -H2n -H1n #Ht1 //
50 | lapply (unwind2_term_eq_repl_dx f β¦ Ht2) -Ht2 #Ht2
51 @(subset_eq_trans β¦ Ht2) -t2
52 @(subset_eq_trans β¦ (unwind2_term_fsubst β¦))
53 [ @fsubst_eq_repl [ // | // ]
54 @(subset_eq_canc_dx β¦ (unwind2_term_after β¦))
55 @(subset_eq_canc_sn β¦ (unwind2_term_eq_repl_dx β¦))
56 [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
57 @(subset_eq_trans β¦ (unwind2_term_after β¦))
58 @unwind2_term_eq_repl_sn
59 (* Note: crux of the proof begins *)
60 @nstream_eq_inv_ext #m
61 <tr_compose_pap <tr_compose_pap
62 <tr_uni_pap <tr_uni_pap <tr_pap_plus
63 >list_append_rcons_sn in H1n; <reverse_append #H1n
64 lapply (unwind2_rmap_append_pap_closed f β¦ H1n) #H2n
65 >nrplus_inj_dx in β’ (???%); <H2n -H2n
66 lapply (tls_unwind2_rmap_append_closed f β¦ H1n) -H1n #H2n
67 <(tr_pap_eq_repl β¦ H2n) -H2n //
68 (* Note: crux of the proof ends *)
70 | /2 width=2 by ex_intro/
71 | @term_proper_outer #H0 (**) (* full auto does not work *)
72 /3 width=2 by unwind2_term_des_inner/