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/dbfr.ma".
16 include "delayed_updating/reduction/ibfr.ma".
18 include "delayed_updating/unwind/unwind2_constructors.ma".
19 include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
20 include "delayed_updating/unwind/unwind2_preterm_eq.ma".
21 include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
22 include "delayed_updating/unwind/unwind2_rmap_head.ma".
24 include "delayed_updating/substitution/fsubst_eq.ma".
25 include "delayed_updating/substitution/lift_prototerm_eq.ma".
27 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
28 include "delayed_updating/syntax/path_head_structure.ma".
29 include "delayed_updating/syntax/path_structure_depth.ma".
31 (* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
33 (* Main destructions with ibfr **********************************************)
35 theorem dbfr_des_ibfr (f) (t1) (t2) (r): t1 Ļµ š ā
36 t1 ā”ššš[r] t2 ā ā¼[f]t1 ā”š¢šš[ār] ā¼[f]t2.
38 * #p #b #q #h #k #Hr #Hb #Hh #H1k #Ht1 #Ht2 destruct
39 @(ex6_5_intro ā¦ (āp) (āb) (āq) (āb) (āāq))
40 [ -H0t1 -Hb -Hh -H1k -Ht1 -Ht2 //
41 | -H0t1 -Hh -H1k -Ht1 -Ht2 //
42 | -H0t1 -Hb -Ht1 -H1k -Ht2
43 >Hh in ā¢ (??%?); >path_head_structure_depth <Hh -Hh //
44 | -H0t1 -Hb -Hh -Ht1 -Ht2
46 >H1k in ā¢ (??%?); >path_head_structure_depth <H1k -H1k //
47 | lapply (in_comp_unwind2_path_term f ā¦ Ht1) -Ht2 -Ht1 -H0t1 -Hb -Hh
48 <unwind2_path_d_dx >list_append_rcons_dx >list_append_assoc
49 lapply (unwind2_rmap_append_pap_closed f ā¦ (pāšāb) ā¦ H1k) -H1k
51 lapply (eq_inv_ninj_bi ā¦ H2k) -H2k #H2k <H2k -H2k #Ht1 //
52 | lapply (unwind2_term_eq_repl_dx f ā¦ Ht2) -Ht2 #Ht2
53 lapply (path_head_refl_append_bi ā¦ Hh H1k) -Hh -H1k <nrplus_inj_sn #H1k
54 @(subset_eq_trans ā¦ Ht2) -t2
55 @(subset_eq_trans ā¦ (unwind2_term_fsubst_ppc ā¦))
56 [ @fsubst_eq_repl [ // | // ]
57 @(subset_eq_trans ā¦ (unwind2_term_iref ā¦))
58 @(subset_eq_canc_sn ā¦ (lift_term_eq_repl_dx ā¦))
59 [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
60 @(subset_eq_trans ā¦ (lift_unwind2_term_after ā¦))
61 @unwind2_term_eq_repl_sn
62 (* Note: crux of the proof begins *)
64 @(stream_eq_trans ā¦ (tr_compose_uni_dx ā¦))
66 [ <unwind2_rmap_append_pap_closed //
67 <depth_append <depth_L_sn
68 <nplus_comm <nrplus_npsucc_sn <nplus_succ_sn //
70 /2 width=1 by tls_unwind2_rmap_closed/
72 (* Note: crux of the proof ends *)
74 | /2 width=2 by ex_intro/