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=cd21acf66ae962333918f0a426ad930587ed1872;hpb=12d58352dbd62df65d44becc0f69fc5a7b370866;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 cd21acf66..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
@@ -19,53 +19,53 @@ 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_xap_le_closed (f) (p) (q) (n) (k):
-      p = (↳[n]p)●q → k ≤ n →
-      (▶[f]p)＠❨k❩ = (▶[f]↳[n]p)＠❨k❩.
-#f #p elim p -p
-[ #q #n #k #Hq #Hk
-  elim (eq_inv_list_empty_append … Hq) -Hq * #_ //
-| #l #p #IH #q #n @(nat_ind_succ … n) -n
-  [ #k #_ #Hk <(nle_inv_zero_dx … Hk) -k -IH
-   <path_head_zero <unwind2_rmap_empty //
-  | #n #_ #k cases l [ #m ]
-    [ <path_head_d_sn <list_append_lcons_sn #Hq #Hk
+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_sn <unwind2_rmap_d_sn
+      <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_sn <list_append_lcons_sn #Hq #Hk
+    | <path_head_m_dx #Hq #Hm
       elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
-      <unwind2_rmap_m_sn <unwind2_rmap_m_sn
+      <unwind2_rmap_m_dx <unwind2_rmap_m_dx
       /2 width=2 by/
-    | <path_head_L_sn <list_append_lcons_sn #Hq
-      @(nat_ind_succ … k) -k // #k #_ #Hk
-      lapply (nle_inv_succ_bi … Hk) -Hk #Hk
+    | <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_sn <unwind2_rmap_L_sn
+      <unwind2_rmap_L_dx <unwind2_rmap_L_dx
       <tr_xap_push <tr_xap_push
       /3 width=2 by eq_f/
-    | <path_head_A_sn <list_append_lcons_sn #Hq #Hk
+    | <path_head_A_dx #Hq #Hm
       elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
-      <unwind2_rmap_A_sn <unwind2_rmap_A_sn
+      <unwind2_rmap_A_dx <unwind2_rmap_A_dx
       /2 width=2 by/
-    | <path_head_S_sn <list_append_lcons_sn #Hq #Hk
+    | <path_head_S_dx #Hq #Hm
       elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
-      <unwind2_rmap_S_sn <unwind2_rmap_S_sn
+      <unwind2_rmap_S_dx <unwind2_rmap_S_dx
       /2 width=2 by/
     ]
   ]
 ]
 qed-.
 
-lemma unwind2_rmap_head_append_xap_closed (f) (p) (q) (n):
-      p = ↳[n](p●q) →
+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-.
@@ -76,60 +76,59 @@ lemma unwind2_rmap_head_xap (f) (p) (n):
 [ #n <path_head_empty <unwind2_rmap_labels_L <height_labels_L
   <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_xap <tr_uni_xap_succ //
-  | <unwind2_rmap_m_sn <path_head_m_sn <height_m_sn //
-  | <unwind2_rmap_L_sn <path_head_L_sn <height_L_sn
-    <tr_xap_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) (n:pnat):
-      p = ↳[n](p●q) →
-      ♭p = ninj (▶[f](p●q)＠⧣❨n❩).
-#f #p #q #n #Hn
->tr_xap_ninj >Hn in ⊢ (??%?);
->(unwind2_rmap_head_append_xap_closed … Hn) -Hn
+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) (k):
-      p = (↳[n]p)●q →
-      ⇂*[k]▶[f]q ≗ ⇂*[n+k]▶[f]p.
-#f #p elim p -p
-[ #q #n #k #Hq
-  elim (eq_inv_list_empty_append … Hq) -Hq #Hn #H0 destruct
-  <path_head_empty in Hn; #Hn
-  <(eq_inv_empty_labels … Hn) -n //
-| #l #p #IH #q #n @(nat_ind_succ … n) -n //
-  #n #_ #k cases l [ #m ]
-  [ <path_head_d_sn <list_append_lcons_sn #Hq
+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_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_sn <list_append_lcons_sn #Hq
+  | <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_sn <list_append_lcons_sn #Hq
+  | <path_head_L_dx #Hq
     elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
-    <unwind2_rmap_L_sn <nplus_succ_sn /2 width=1 by/
-  | <path_head_A_sn <list_append_lcons_sn #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_sn /2 width=2 by/
-  | <path_head_S_sn <list_append_lcons_sn #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_sn /2 width=2 by/
+    <unwind2_rmap_S_dx /2 width=2 by/
   ]
 ]
 qed-.
 
-lemma tls_unwind2_rmap_append_closed (f) (p) (q) (n):
-      p = ↳[n](p●q) →
-      ▶[f]q ≗ ⇂*[n]▶[f](p●q).
+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.