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".
26 include "delayed_updating/substitution/lift_path_head.ma".
28 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
31 (* DELAYED FOCUSED REDUCTION ************************************************)
33 (* Constructions with lift **************************************************)
36 ↑[↑[r]f](rᴿ) = (↑[f]r)ᴿ.
37 #f #r @(list_ind_rcons … r) -r //
39 [ <reverse_rcons <lift_path_d_sn <lift_rmap_d_dx
40 <lift_path_d_dx <reverse_rcons
44 theorem dfr_lift_bi (f) (p) (q) (t1) (t2): (*t1 ϵ 𝐓 → *)
45 t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[↑[f]p,↑[↑[p◖𝗔◖𝗟]f]q] ↑[f]t2.
48 @(ex_intro … ((↑[p●𝗔◗𝗟◗q]f)@⧣❨n❩)) @and3_intro
50 <lift_rmap_L_dx >lift_path_L_sn
51 >list_append_rcons_sn in H1n; <reverse_append #H1n
52 <(lift_path_head … H1n) -H1n //
54 | lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
55 <unwind2_path_d_dx <depth_structure
56 >list_append_rcons_sn in H1n; <reverse_append #H1n
57 lapply (unwind2_rmap_append_pap_closed f … H1n)
58 <reverse_lcons <depth_L_dx #H2n
59 lapply (eq_inv_ninj_bi … H2n) -H2n #H2n <H2n -H2n -H1n #Ht1 //
60 | lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
61 @(subset_eq_trans … Ht2) -t2
62 @(subset_eq_trans … (unwind2_term_fsubst …))
63 [ @fsubst_eq_repl [ // | // ]
64 @(subset_eq_trans … (unwind2_term_iref …))
65 @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
66 [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
67 @(subset_eq_trans … (unwind2_lift_term_after …))
68 @unwind2_term_eq_repl_sn
69 (* Note: crux of the proof begins *)
70 @nstream_eq_inv_ext #m
71 <tr_compose_pap <tr_compose_pap
72 <tr_uni_pap <tr_uni_pap <tr_pap_plus
73 >list_append_rcons_sn in H1n; <reverse_append #H1n
74 lapply (unwind2_rmap_append_pap_closed f … H1n) #H2n
75 >nrplus_inj_dx in ⊢ (???%); <H2n -H2n
76 lapply (tls_unwind2_rmap_append_closed f … H1n) #H2n
77 <(tr_pap_eq_repl … H2n) -H2n -H1n //
78 (* Note: crux of the proof ends *)
80 | /2 width=2 by ex_intro/