matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma

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   3 (*      ||M||                                                             *)
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  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "delayed_updating/unwind/unwind2_path_eq.ma".
  16 include "delayed_updating/substitution/lift_path_prelift.ma".
  17
  18 (* UNWIND FOR PATH **********************************************************)
  19
  20 (* Constructions with lift_path *********************************************)
  21
  22 lemma lift_unwind2_path_after (p) (f1) (f2):
  23       ↑[f2]▼[f1]p = ▼[f2∘f1]p.
  24 #p @(path_ind_unwind … p) -p // [ #n | #p ] #IH #f1 #f2
  25 [ <unwind2_path_d_empty <unwind2_path_d_empty
  26   <lift_path_d_sn <lift_path_empty //
  27 | <unwind2_path_L_sn <unwind2_path_L_sn <lift_path_L_sn
  28   >tr_compose_push_bi //
  29 ]
  30 qed.
  31
  32 lemma unwind2_path_after_lift (p) (f1) (f2):
  33       ▼[f2]↑[f1]p = ▼[f2∘f1]p.
  34 #p @(path_ind_unwind … p) -p // [ #n #l ] #p #IH #f1 #f2
  35 [ <lift_path_d_sn <unwind2_path_d_lcons
  36   <lift_path_lcons_prelift <unwind2_path_d_lcons >lift_path_lcons_prelift
  37   >IH -IH
  38   >(unwind2_path_eq_repl … (tr_compose_assoc …))
  39   >(unwind2_path_eq_repl … (tr_compose_assoc …))
  40   <unwind2_path_after <unwind2_path_after in ⊢ (???%);
  41   /3 width=1 by unwind2_path_eq_repl, eq_f/
  42 | <lift_path_m_sn <unwind2_path_m_sn <unwind2_path_m_sn //
  43 | <lift_path_L_sn <unwind2_path_L_sn <unwind2_path_L_sn
  44   >tr_compose_push_bi //
  45 ]
  46 qed.