matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_closed.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "delayed_updating/substitution/lift_rmap_eq.ma".
  16 include "delayed_updating/syntax/path_closed.ma".
  17 include "ground/lib/stream_eq_eq.ma".
  18
  19 (* LIFT MAP FOR PATH ********************************************************)
  20
  21 (* Destructions with cpp ****************************************************)
  22
  23 lemma tls_plus_lift_rmap_closed (f) (q) (n):
  24       q ϵ 𝐂❨n❩ →
  25       ∀m. ⇂*[m]f ≗ ⇂*[m+n]↑[q]f.
  26 #f #q #n #Hq elim Hq -q -n //
  27 #q #n #_ #IH #m
  28 <nplus_succ_dx <stream_tls_swap //
  29 qed-.
  30
  31 lemma tls_lift_rmap_closed (f) (q) (n):
  32       q ϵ 𝐂❨n❩ →
  33       f ≗ ⇂*[n]↑[q]f.
  34 #f #q #n #H0
  35 /2 width=1 by tls_plus_lift_rmap_closed/
  36 qed-.
  37
  38 lemma tls_succ_lift_rmap_append_L_closed_dx (f) (p) (q) (n):
  39       q ϵ 𝐂❨n❩ →
  40       ↑[p]f ≗ ⇂*[↑n]↑[p●𝗟◗q]f.
  41 #f #p #q #n #Hq
  42 /3 width=1 by tls_lift_rmap_closed, pcc_L_sn/
  43 qed-.