include "delayed_updating/reduction/dfr.ma".
include "delayed_updating/reduction/ifr.ma".
-include "delayed_updating/substitution/fsubst_lift.ma".
+
+include "delayed_updating/unwind1/unwind_fsubst.ma".
+include "delayed_updating/unwind1/unwind_constructors.ma".
+include "delayed_updating/unwind1/unwind_preterm_eq.ma".
+include "delayed_updating/unwind1/unwind_structure_depth.ma".
+include "delayed_updating/unwind1/unwind_depth.ma".
+
include "delayed_updating/substitution/fsubst_eq.ma".
-include "delayed_updating/substitution/lift_constructors.ma".
-include "delayed_updating/substitution/lift_preterm_eq.ma".
-include "delayed_updating/substitution/lift_structure_depth.ma".
-include "delayed_updating/substitution/lift_depth.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
include "delayed_updating/syntax/prototerm_proper_constructors.ma".
include "delayed_updating/syntax/path_structure_depth.ma".
include "ground/relocation/tr_uni_compose.ma".
(* DELAYED FOCUSED REDUCTION ************************************************)
-lemma tr_uni_eq_repl (n1) (n2):
- n1 = n2 → 𝐮❨n1❩ ≗ 𝐮❨n2❩.
-// qed.
-
+(* COMMENT
axiom pippo (b) (q) (n):
↑❘q❘ = (↑[q]𝐢)@❨n❩ →
↑❘q❘+❘b❘= (↑[b●𝗟◗q]𝐢)@❨n+❘b❘❩.
-lemma lift_rmap_tls_eq_id (p) (n):
+lemma unwind_rmap_tls_eq_id (p) (n):
❘p❘ = ↑[p]𝐢@❨n❩ →
(𝐢) ≗ ⇂*[n]↑[p]𝐢.
#p @(list_ind_rcons … p) -p
[ #n <depth_empty #H destruct
| #p * [ #m ] #IH #n
- [ <depth_d_dx <lift_rmap_pap_d_dx #H0
- @(stream_eq_trans … (lift_rmap_tls_d_dx …))
+ [ <depth_d_dx <unwind_rmap_pap_d_dx #H0
+ @(stream_eq_trans … (unwind_rmap_tls_d_dx …))
@(stream_eq_trans … (IH …)) -IH //
| /2 width=1 by/
- | <depth_L_dx <lift_rmap_L_dx
+ | <depth_L_dx <unwind_rmap_L_dx
cases n -n [| #n ] #H0
[
|
(* (↑❘q❘+❘b❘=↑[b●𝗟◗q]𝐢@❨n+❘b❘❩ *)
(* [↑[p]𝐢@❨n❩]⫯*[❘p❘]f∘⇂*[n]↑[p]𝐢) *)
-lemma lift_rmap_tls_eq (f) (p) (n):
+lemma unwind_rmap_tls_eq (f) (p) (n):
❘p❘ = ↑[p]𝐢@❨n❩ →
f ≗ ⇂*[n]↑[p]f.
#f #p #n #Hp
@(stream_eq_canc_dx … (stream_tls_eq_repl …))
-[| @lift_rmap_decompose | skip ]
+[| @unwind_rmap_decompose | skip ]
<tr_compose_tls <Hp
-@(stream_eq_canc_dx) … (lift_rmap_decompose …))
+@(stream_eq_canc_dx) … (unwind_rmap_decompose …))
-lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
- t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[⊗p,⊗q] ↑[f]t2.
-#f #p #q #t1 #t2 #H0t1
-* #b #n * #Hb #Hn #Ht1 #Ht2
-@(ex1_2_intro … (⊗b) (↑❘⊗q❘)) @and4_intro
+*)
+lemma dfr_unwind_id_bi (p) (q) (t1) (t2): t1 ϵ 𝐓 →
+ t1 ➡𝐝𝐟[p,q] t2 → ▼[𝐢]t1 ➡𝐟[⊗p,⊗q] ▼[𝐢]t2.
+#p #q #t1 #t2 #H0t1
+* #b #n * #Hb #Hn #Ht1 #Ht2
+@(ex1_2_intro … (⊗b) (↑♭⊗q)) @and4_intro
[ //
-| #g <lift_rmap_structure <depth_structure
- >tr_pushs_swap <tr_pap_pushs_le //
-| lapply (in_comp_lift_bi f … Ht1) -Ht1 -H0t1 -Hb -Ht2
- <lift_path_d_empty_dx //
-| lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
+| (*//*)
+| lapply (in_comp_unwind_bi (𝐢) … Ht1) -Ht1 -H0t1 -Hb -Ht2
+ <unwind_path_d_empty_dx <depth_structure //
+| lapply (unwind_term_eq_repl_dx (𝐢) … Ht2) -Ht2 #Ht2
@(subset_eq_trans … Ht2) -t2
- @(subset_eq_trans … (lift_fsubst …))
- [ <lift_rmap_append <lift_rmap_A_sn (* <lift_rmap_append <lift_rmap_L_sn *)
+ @(subset_eq_trans … (unwind_fsubst …))
+ [ (*<unwind_rmap_append <unwind_rmap_A_sn <unwind_rmap_append <unwind_rmap_L_sn *)
<structure_append <structure_A_sn <structure_append <structure_L_sn
<depth_append <depth_L_sn <depth_structure <depth_structure
@fsubst_eq_repl [ // ]
- @(subset_eq_trans … (lift_iref …))
+ @(subset_eq_trans … (unwind_iref …))
+
+ elim Hb -Hb #Hb #H0 <H0 -H0 <nrplus_zero_dx <nplus_zero_dx <nsucc_unfold
+ >Hn
@(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
- [ @lift_grafted_S /2 width=2 by ex_intro/ | skip ]
- @(subset_eq_trans … (lift_term_after …))
- @(subset_eq_canc_dx … (lift_term_after …))
- @lift_term_eq_repl_sn -t1
+ [ @unwind_grafted_S /2 width=2 by ex_intro/ | skip ]
+ <Hn <Hn
+(*
+ @(subset_eq_trans … (lift_term_eq_repl_dx …))
+ [ @(unwind_term_eq_repl_sn … (tls_succ_unwind q …)) | skip ]
+*)
+(*
+
+ @subset_eq_trans
+ [2: @unwind_term_eq_repl_dx
+ @(subset_eq_canc_sn … (unwind_term_eq_repl_dx …))
+
+ @(subset_eq_canc_sn … (unwind_term_eq_repl_dx …))
+ [ @unwind_grafted_S /2 width=2 by ex_intro/ | skip ]
+
+ @(subset_eq_trans … (unwind_term_after …))
+ @(subset_eq_canc_dx … (unwind_term_after …))
+ @unwind_term_eq_repl_sn -t1
@(stream_eq_trans … (tr_compose_uni_dx …))
lapply (Hn (𝐢)) -Hn >tr_id_unfold #Hn
lapply (pippo … b … Hn) -Hn #Hn
@tr_compose_eq_repl
- [ <lift_rmap_pap_le //
+ [ <unwind_rmap_pap_le //
<Hn <nrplus_inj_sn //
|
]
+*)
| //
| /2 width=2 by ex_intro/
| //
]
]
+
+(*
+Hn : ↑❘q❘ = ↑[p●𝗔◗b●𝗟◗q]𝐢@❨n❩
+---------------------------
+↑[𝐮❨↑❘q❘+❘b❘❩] ↑[↑[p]𝐢] t ⇔ ↑[𝐮❨↑[p●𝗔◗b●𝗟◗q]𝐢@❨n+❘b❘❩❩] t
+*)
+(*
+(↑[𝐮❨↑❘q❘❩]▼[⇂*[↑❘q❘]▼[p●𝗟◗q]𝐢](t1⋔(p◖𝗦))⇔▼[𝐮❨↑❘q❘❩∘▼[p●𝗔◗b●𝗟◗q]𝐢](t1⋔(p◖𝗦))
+*)