matita/matita/contribs/lambdadelta/delayed_updating/unwind0/unwind1_path_structure.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "delayed_updating/unwind0/unwind1_rmap_eq.ma".
  16 include "delayed_updating/unwind0/unwind1_path.ma".
  17 include "delayed_updating/substitution/lift_structure.ma".
  18
  19 (* BASIC UNWIND FOR PATH ****************************************************)
  20
  21 (* Constructions with structure *********************************************)
  22
  23 fact unwind1_path_d_dx_aux (k) (p) (n):
  24      k = ❘p❘ → (⊗p)◖𝗱((▶p)@❨n❩) = ▼(p◖𝗱n).
  25 #k @(nat_ind_succ … k) -k
  26 [ #p #n #H0 >(list_length_inv_zero_sn … H0) -p //
  27 | #k #IH *
  28   [ #n #H0 elim (eq_inv_nsucc_zero … H0)
  29   | * [ #m ] #p #n #H0
  30     lapply (eq_inv_nsucc_bi … H0) -H0
  31     [ cases p -p [ -IH | #l #p ] #H0 destruct <unwind1_path_d_lcons
  32       [ <lift_path_d_sn <lift_path_empty <unwind1_path_d_empty
  33         <list_cons_comm <(tr_pap_eq_repl … (unwind1_rmap_d_empty …)) //
  34       | >list_cons_shift <lift_path_d_dx <IH -IH //
  35         <structure_lift <structure_d_sn /3 width=1 by eq_f2/
  36       ]
  37     | #H0 destruct <unwind1_path_m_sn <IH -IH //
  38     | #H0 destruct <unwind1_path_L_sn <IH -IH //
  39     | #H0 destruct <unwind1_path_A_sn <IH -IH //
  40     | #H0 destruct <unwind1_path_S_sn <IH -IH //
  41     ]
  42   ]
  43 ]
  44 qed-.
  45
  46 lemma unwind1_path_d_dx (p) (n):
  47       (⊗p)◖𝗱((▶p)@❨n❩) = ▼(p◖𝗱n).
  48 /2 width=2 by unwind1_path_d_dx_aux/ qed.