update in delayd_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / unwind / unwind2_rmap_head.ma

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
deleted file mode 100644 (file)
index 416c6e7..0000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.ma
+++ /dev/null
@@ -1,134 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "delayed_updating/unwind/unwind2_rmap_labels.ma".
-include "delayed_updating/unwind/unwind2_rmap_eq.ma".
-include "delayed_updating/syntax/path_head_depth.ma".
-include "ground/relocation/xap.ma".
-include "ground/lib/stream_eq_eq.ma".
-include "ground/arith/nat_le_plus.ma".
-
-(* TAILED UNWIND FOR RELOCATION MAP *****************************************)
-
-(* Constructions with path_head *********************************************)
-
-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_xap_pushs_le //
-| #l #p #IH #n @(nat_ind_succ … n) -n //
-  #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.