X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Funwind%2Funwind2_rmap_head.ma;h=416c6e7924650b412ad854cb119265877fe14151;hb=41a54a797af98d2867d4bf979d424283fb44a1fc;hp=579cbd514cf20c90426d0d9dcb320a2e474e9833;hpb=dfcad1c1a698bac1b7fb6a5f59393b28f45182af;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.ma
index 579cbd514..416c6e792 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.ma
@@ -13,28 +13,122 @@
 (**************************************************************************)
 
 include "delayed_updating/unwind/unwind2_rmap_labels.ma".
-include "delayed_updating/unwind/nap.ma".
+include "delayed_updating/unwind/unwind2_rmap_eq.ma".
 include "delayed_updating/syntax/path_head_depth.ma".
-include "delayed_updating/syntax/path_height.ma".
+include "ground/relocation/xap.ma".
+include "ground/lib/stream_eq_eq.ma".
+include "ground/arith/nat_le_plus.ma".
 
-(* UNWIND MAP FOR PATH ******************************************************)
+(* TAILED UNWIND FOR RELOCATION MAP *****************************************)
 
 (* Constructions with path_head *********************************************)
 
-lemma unwind2_rmap_head_push (f) (p) (n):
-      n + ♯(↳[n]p) = (▶[⫯f]↳[n]p)@↑❨n❩.
+lemma unwind2_rmap_head_xap_le_closed (f) (p) (q) (n) (m):
+      q = ↳[n]q → m ≤ n →
+      ▶[f](p●q)＠❨m❩ = ▶[f]↳[n](p●q)＠❨m❩.
+#f #p #q elim q -q
+[ #n #m #Hq
+  <(eq_inv_path_empty_head … Hq) -n #Hm
+  <(nle_inv_zero_dx … Hm) -m //
+| #l #q #IH #n @(nat_ind_succ … n) -n
+  [ #m #_ #Hm <(nle_inv_zero_dx … Hm) -m -IH //
+  | #n #_ #m cases l [ #k ]
+    [ <path_head_d_dx #Hq #Hm
+      elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+      <unwind2_rmap_d_dx <unwind2_rmap_d_dx
+      <tr_compose_xap <tr_compose_xap
+      @(IH … Hq) -IH -Hq (**) (* auto too slow *)
+      @nle_trans [| @tr_uni_xap ]
+      /2 width=1 by nle_plus_bi_dx/
+    | <path_head_m_dx #Hq #Hm
+      elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+      <unwind2_rmap_m_dx <unwind2_rmap_m_dx
+      /2 width=2 by/
+    | <path_head_L_dx #Hq
+      @(nat_ind_succ … m) -m // #m #_ #Hm
+      lapply (nle_inv_succ_bi … Hm) -Hm #Hm
+      elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+      <unwind2_rmap_L_dx <unwind2_rmap_L_dx
+      <tr_xap_push <tr_xap_push
+      /3 width=2 by eq_f/
+    | <path_head_A_dx #Hq #Hm
+      elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+      <unwind2_rmap_A_dx <unwind2_rmap_A_dx
+      /2 width=2 by/
+    | <path_head_S_dx #Hq #Hm
+      elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+      <unwind2_rmap_S_dx <unwind2_rmap_S_dx
+      /2 width=2 by/
+    ]
+  ]
+]
+qed-.
+
+lemma unwind2_rmap_head_xap_closed (f) (p) (q) (n):
+      q = ↳[n]q →
+      ▶[f](p●q)＠❨n❩ = ▶[f]↳[n](p●q)＠❨n❩.
+/2 width=2 by unwind2_rmap_head_xap_le_closed/
+qed-.
+
+lemma unwind2_rmap_head_xap (f) (p) (n):
+      n + ♯(↳[n]p) = (▶[f]↳[n]p)＠❨n❩.
 #f #p elim p -p
 [ #n <path_head_empty <unwind2_rmap_labels_L <height_labels_L
-  >tr_pushs_swap <tr_nap_pushs_lt //
+  <tr_xap_pushs_le //
 | #l #p #IH #n @(nat_ind_succ … n) -n //
-  #n #_ cases l [ #m ]
-  [ <unwind2_rmap_d_sn <path_head_d_sn <height_d_sn
-    <nplus_assoc >IH -IH <tr_compose_nap //
-  | <unwind2_rmap_m_sn <path_head_m_sn <height_m_sn //
-  | <unwind2_rmap_L_sn <path_head_L_sn <height_L_sn
-    <tr_nap_push <npred_succ //
-  | <unwind2_rmap_A_sn <path_head_A_sn <height_A_sn //
-  | <unwind2_rmap_S_sn <path_head_S_sn <height_S_sn //
+  #n #_ cases l [ #k ]
+  [ <unwind2_rmap_d_dx <path_head_d_dx <height_d_dx
+    <nplus_comm in ⊢ (??(??%)?); <nplus_assoc
+    >IH -IH <tr_compose_xap <tr_uni_xap_succ //
+  | <unwind2_rmap_m_dx <path_head_m_dx <height_m_dx //
+  | <unwind2_rmap_L_dx <path_head_L_dx <height_L_dx
+    <tr_xap_push <npred_succ <nplus_succ_sn //
+  | <unwind2_rmap_A_dx <path_head_A_dx <height_A_dx //
+  | <unwind2_rmap_S_dx <path_head_S_dx <height_S_dx //
   ]
 ]
 qed.
+
+lemma unwind2_rmap_append_pap_closed (f) (p) (q) (h:pnat):
+      q = ↳[h]q →
+      ♭q = ninj (▶[f](p●q)＠⧣❨h❩).
+#f #p #q #h #Hh
+>tr_xap_ninj >(path_head_refl_append_sn p … Hh) in ⊢ (??%?);
+>(unwind2_rmap_head_xap_closed … Hh) -Hh
+<path_head_depth //
+qed.
+
+lemma tls_unwind2_rmap_plus_closed (f) (p) (q) (n) (m):
+      q = ↳[n]q →
+      ⇂*[m]▶[f]p ≗ ⇂*[n+m]▶[f](p●q).
+#f #p #q elim q -q
+[ #n #m #Hq
+  <(eq_inv_path_empty_head … Hq) -n //
+| #l #q #IH #n @(nat_ind_succ … n) -n //
+  #n #_ #m cases l [ #k ]
+  [ <path_head_d_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq <nrplus_inj_sn
+    @(stream_eq_trans … (tls_unwind2_rmap_d_dx …))
+    >nrplus_inj_dx >nrplus_inj_sn >nrplus_inj_sn <nplus_plus_comm_23
+    /2 width=1 by/
+  | <path_head_m_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+    <unwind2_rmap_m_sn /2 width=1 by/
+  | <path_head_L_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+    <unwind2_rmap_L_dx <nplus_succ_sn /2 width=1 by/
+  | <path_head_A_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+    <unwind2_rmap_A_dx /2 width=2 by/
+  | <path_head_S_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+    <unwind2_rmap_S_dx /2 width=2 by/
+  ]
+]
+qed-.
+
+lemma tls_unwind2_rmap_closed (f) (p) (q) (n):
+      q = ↳[n]q →
+      ▶[f]p ≗ ⇂*[n]▶[f](p●q).
+/2 width=1 by tls_unwind2_rmap_plus_closed/
+qed.