X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Freduction%2Fdfr_ifr.ma;h=77e303f0504f8bb8bedd81afcb398beb5c424f0b;hb=b15b3e2d9e333bf94677ff2731c825da3566c9ec;hp=5d6c3cfefaf59bf5db8ea16fa83c8c821095b3e4;hpb=2cc4eb5d0210be58286e028278852122dcb68052;p=helm.git

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 5d6c3cfef..77e303f05 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -14,19 +14,99 @@
 
 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/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 * #Hb #Ht1 #Ht2
-@(ex_intro … (⊗b)) @and3_intro
-[ //
-| lapply (in_comp_lift_bi f … Ht1) -Ht1 #Ht1 
+(* 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
+[ //
+| //
+| 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 … (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 …))
+(*
+    @(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
+*)