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".
17 include "delayed_updating/unwind1/unwind_fsubst.ma".
18 include "delayed_updating/unwind1/unwind_constructors.ma".
19 include "delayed_updating/unwind1/unwind_preterm_eq.ma".
20 include "delayed_updating/unwind1/unwind_structure_depth.ma".
21 include "delayed_updating/unwind1/unwind_depth.ma".
22 include "delayed_updating/substitution/fsubst_eq.ma".
23 include "delayed_updating/substitution/lift_prototerm_eq.ma".
24 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
25 include "delayed_updating/syntax/path_structure_depth.ma".
26 include "ground/relocation/tr_uni_compose.ma".
27 include "ground/relocation/tr_pap_pushs.ma".
29 (* DELAYED FOCUSED REDUCTION ************************************************)
32 axiom pippo (b) (q) (n):
34 ↑❘q❘+❘b❘= (↑[b●𝗟◗q]𝐢)@❨n+❘b❘❩.
36 lemma unwind_rmap_tls_eq_id (p) (n):
39 #p @(list_ind_rcons … p) -p
40 [ #n <depth_empty #H destruct
42 [ <depth_d_dx <unwind_rmap_pap_d_dx #H0
43 @(stream_eq_trans … (unwind_rmap_tls_d_dx …))
44 @(stream_eq_trans … (IH …)) -IH //
46 | <depth_L_dx <unwind_rmap_L_dx
47 cases n -n [| #n ] #H0
57 (* (↑❘q❘+❘b❘=↑[b●𝗟◗q]𝐢@❨n+❘b❘❩ *)
58 (* [↑[p]𝐢@❨n❩]⫯*[❘p❘]f∘⇂*[n]↑[p]𝐢) *)
59 lemma unwind_rmap_tls_eq (f) (p) (n):
63 @(stream_eq_canc_dx … (stream_tls_eq_repl …))
64 [| @unwind_rmap_decompose | skip ]
67 @(stream_eq_canc_dx) … (unwind_rmap_decompose …))
70 lemma dfr_unwind_id_bi (p) (q) (t1) (t2): t1 ϵ 𝐓 →
71 t1 ➡𝐝𝐟[p,q] t2 → ▼[𝐢]t1 ➡𝐟[⊗p,⊗q] ▼[𝐢]t2.
73 * #b #n * #Hb #Hn #Ht1 #Ht2
74 @(ex1_2_intro … (⊗b) (↑❘⊗q❘)) @and4_intro
77 | lapply (in_comp_unwind_bi (𝐢) … Ht1) -Ht1 -H0t1 -Hb -Ht2
78 <unwind_path_d_empty_dx <depth_structure //
79 | lapply (unwind_term_eq_repl_dx (𝐢) … Ht2) -Ht2 #Ht2
80 @(subset_eq_trans … Ht2) -t2
81 @(subset_eq_trans … (unwind_fsubst …))
82 [ (*<unwind_rmap_append <unwind_rmap_A_sn <unwind_rmap_append <unwind_rmap_L_sn *)
83 <structure_append <structure_A_sn <structure_append <structure_L_sn
84 <depth_append <depth_L_sn <depth_structure <depth_structure
85 @fsubst_eq_repl [ // ]
86 @(subset_eq_trans … (unwind_iref …))
88 elim Hb -Hb #Hb #H0 <H0 -H0 <nrplus_zero_dx <nplus_zero_dx <Hn
89 @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
90 [ @unwind_grafted_S /2 width=2 by ex_intro/ | skip ]
93 @(subset_eq_canc_sn … (unwind_term_eq_repl_dx …))
94 [ @unwind_grafted_S /2 width=2 by ex_intro/ | skip ]
96 @(subset_eq_trans … (unwind_term_after …))
97 @(subset_eq_canc_dx … (unwind_term_after …))
98 @unwind_term_eq_repl_sn -t1
99 @(stream_eq_trans … (tr_compose_uni_dx …))
100 lapply (Hn (𝐢)) -Hn >tr_id_unfold #Hn
101 lapply (pippo … b … Hn) -Hn #Hn
103 [ <unwind_rmap_pap_le //
104 <Hn <nrplus_inj_sn //
109 | /2 width=2 by ex_intro/
115 Hn : ↑❘q❘ = ↑[p●𝗔◗b●𝗟◗q]𝐢@❨n❩
116 ---------------------------
117 ↑[𝐮❨↑❘q❘+❘b❘❩] ↑[↑[p]𝐢] t ⇔ ↑[𝐮❨↑[p●𝗔◗b●𝗟◗q]𝐢@❨n+❘b❘❩❩] t