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".
28 include "delayed_updating/syntax/path_head_structure.ma".
29 include "delayed_updating/syntax/path_structure_depth.ma".
30 include "delayed_updating/syntax/path_structure_reverse.ma".
31 include "delayed_updating/syntax/path_depth_reverse.ma".
33 (* DELAYED FOCUSED REDUCTION ************************************************)
35 (* Main destructions with ifr ***********************************************)
37 theorem dfr_des_ifr (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
38 t1 ➡𝐝𝐟[p,q] t2 → ▼[f]t1 ➡𝐟[⊗p,⊗q] ▼[f]t2.
39 #f #p #q #t1 #t2 #H0t1
41 @(ex_intro … (↑♭⊗q)) @and3_intro
42 [ -H0t1 -H1n -Ht1 -Ht2
43 >list_append_rcons_sn <reverse_append
44 >nsucc_unfold >depth_reverse >depth_L_dx >reverse_lcons
45 >structure_L_sn >structure_reverse
46 <path_head_structure //
47 | lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
48 <unwind2_path_d_dx <depth_structure
49 >list_append_rcons_sn in H1n; <reverse_append #H1n
50 lapply (unwind2_rmap_append_pap_closed f … H1n)
51 <reverse_lcons <depth_L_dx #H2n
52 lapply (eq_inv_ninj_bi … H2n) -H2n #H2n <H2n -H2n -H1n #Ht1 //
53 | lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
54 @(subset_eq_trans … Ht2) -t2
55 @(subset_eq_trans … (unwind2_term_fsubst …))
56 [ @fsubst_eq_repl [ // | // ]
57 @(subset_eq_trans … (unwind2_term_iref …))
58 @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
59 [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
60 @(subset_eq_trans … (unwind2_lift_term_after …))
61 @unwind2_term_eq_repl_sn
62 (* Note: crux of the proof begins *)
63 @nstream_eq_inv_ext #m
64 <tr_compose_pap <tr_compose_pap
65 <tr_uni_pap <tr_uni_pap <tr_pap_plus
66 >list_append_rcons_sn in H1n; <reverse_append #H1n
67 lapply (unwind2_rmap_append_pap_closed f … H1n) #H2n
68 >nrplus_inj_dx in ⊢ (???%); <H2n -H2n
69 lapply (tls_unwind2_rmap_append_closed f … H1n) #H2n
70 <(tr_pap_eq_repl … H2n) -H2n -H1n //
71 (* Note: crux of the proof ends *)
73 | /2 width=2 by ex_intro/