WIP in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / reduction / dfr_ifr.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
index c555072f6558176f3d9d046ffb611e37fcf778c0..dd24f856863792f367b106e4354464ede5961645 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -14,30 +14,105 @@
 
 include "delayed_updating/reduction/dfr.ma".
 include "delayed_updating/reduction/ifr.ma".
-include "delayed_updating/substitution/fsubst_lift.ma".
-include "delayed_updating/substitution/lift_structure_depth.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_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".
 include "ground/relocation/tr_pap_pushs.ma".
 
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
-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
+(* COMMENT
+axiom pippo (b) (q) (n):
+      ↑❘q❘ = (↑[q]𝐢)@❨n❩ →
+      ↑❘q❘+❘b❘= (↑[b●𝗟◗q]𝐢)@❨n+❘b❘❩.
+
+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 <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 <unwind_rmap_L_dx
+    cases n -n [| #n ] #H0
+    [
+    | 
+    ]
+  | /2 width=1 by/
+  | /2 width=1 by/
+  ]
+]
+
+
+(*  (↑❘q❘+❘b❘=↑[b●𝗟◗q]𝐢@❨n+❘b❘❩ *)
+(* [↑[p]𝐢@❨n❩]⫯*[❘p❘]f∘⇂*[n]↑[p]𝐢) *)
+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 …))
+[| @unwind_rmap_decompose | skip ]
+<tr_compose_tls <Hp
+
+@(stream_eq_canc_dx) … (unwind_rmap_decompose …)) 
+
+*)
+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_d_empty_dx //
-| lapply (eq_lift_bi 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 …))
-  [ <structure_append <structure_A_sn <structure_append <structure_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 … (unwind_iref …))
+
+    elim Hb -Hb #Hb #H0 <H0 -H0 <nrplus_zero_dx <nplus_zero_dx <Hn
+    @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
+    [ @unwind_grafted_S /2 width=2 by ex_intro/ | skip ]
+
+(*
+    @(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
+    [ <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
+*)