matita/matita/contribs/lambdadelta/delayed_updating/etc/height/unwind2_rmap_closed_height.etc

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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "delayed_updating/unwind/unwind2_rmap_closed.ma".
  16 include "delayed_updating/syntax/path_closed_height.ma".
  17
  18 (* TAILED UNWIND FOR RELOCATION MAP *****************************************)
  19
  20 (* Destructions with cpp and height *****************************************)
  21
  22 lemma nap_depth_unwind2_rmap_closed (o) (f) (q) (n):
  23       q ϵ 𝐂❨o,n❩ →
  24       f＠§❨♯q❩+♭q = ▶[f]q＠§❨♭q❩.
  25 #o #f #q #n #Hq
  26 <(path_closed_des_depth … Hq) in ⊢ (???%);
  27 /2 width=2 by nap_plus_unwind2_rmap_closed_depth/
  28 qed-.
  29
  30 lemma tls_depth_unwind2_rmap_closed (o) (f) (q) (n):
  31       q ϵ 𝐂❨o,n❩ →
  32       ⇂*[♯q]f ≗ ⇂*[♭q]▶[f]q.
  33 #o #f #q #n #Hq elim Hq -q -n //
  34 #q #n #k #_
  35 >(npsucc_pred k) in ⊢ (%→?); <nplus_succ_dx #Hq #IH
  36 <height_d_dx <depth_d_dx
  37 >(path_closed_des_succ_depth … Hq)
  38 @(stream_eq_trans … (tls_unwind2_rmap_d_dx …))
  39 >nrplus_inj_dx >nrplus_inj_sn >nsucc_unfold
  40 <(path_closed_des_succ_depth … Hq) -Hq
  41 <nplus_comm <stream_tls_plus
  42 <nplus_comm <stream_tls_plus
  43 /2 width=1 by stream_tls_eq_repl/
  44 qed-.