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/dfr.ma".
16 include "delayed_updating/reduction/ifr.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".
29 (* DELAYED FOCUSED REDUCTION ************************************************)
31 (* Constructions with lift **************************************************)
33 theorem dfr_lift_bi (f) (p) (q) (t1) (t2): (*t1 Ļµ š ā *)
34 t1 ā”šš[p,q] t2 ā ā[f]t1 ā”š[ā[f]p,ā[ā[pāšāš]f]q] ā[f]t2.
37 @(ex_intro ā¦ ((ā[pāšāšāq]f)ļ¼ ā§£āØnā©)) @and3_intro
39 >H1n >path_head_structure_depth <H1n -H1n //
40 | lapply (in_comp_unwind2_path_term f ā¦ Ht1) -Ht2 -Ht1 -H0t1
41 <unwind2_path_d_dx <depth_structure
42 >list_append_rcons_sn in H1n; <reverse_append #H1n
43 lapply (unwind2_rmap_append_pap_closed f ā¦ H1n)
44 <reverse_lcons <depth_L_dx #H2n
45 lapply (eq_inv_ninj_bi ā¦ H2n) -H2n #H2n <H2n -H2n -H1n #Ht1 //
46 | lapply (unwind2_term_eq_repl_dx f ā¦ Ht2) -Ht2 #Ht2
47 @(subset_eq_trans ā¦ Ht2) -t2
48 @(subset_eq_trans ā¦ (unwind2_term_fsubst ā¦))
49 [ @fsubst_eq_repl [ // | // ]
50 @(subset_eq_trans ā¦ (unwind2_term_iref ā¦))
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¦ (unwind2_lift_term_after ā¦))
54 @unwind2_term_eq_repl_sn
55 (* Note: crux of the proof begins *)
56 @nstream_eq_inv_ext #m
57 <tr_compose_pap <tr_compose_pap
58 <tr_uni_pap <tr_uni_pap <tr_pap_plus
59 >list_append_rcons_sn in H1n; <reverse_append #H1n
60 lapply (unwind2_rmap_append_pap_closed f ā¦ H1n) #H2n
61 >nrplus_inj_dx in ā¢ (???%); <H2n -H2n
62 lapply (tls_unwind2_rmap_append_closed f ā¦ H1n) #H2n
63 <(tr_pap_eq_repl ā¦ H2n) -H2n -H1n //
64 (* Note: crux of the proof ends *)
66 | /2 width=2 by ex_intro/