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

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   3 (*      ||M||                                                             *)
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  14
  15 include "delayed_updating/substitution/lift_rmap.ma".
  16 include "ground/relocation/tr_pn_eq.ma".
  17 include "ground/lib/stream_tls_plus.ma".
  18 include "ground/lib/stream_tls_eq.ma".
  19 include "ground/arith/nat_plus_rplus.ma".
  20 include "ground/arith/nat_rplus_pplus.ma".
  21
  22 (* LIFT FOR RELOCATION MAP **************************************************)
  23
  24 (* Constructions with lift_eq ***********************************************)
  25
  26 lemma lift_rmap_eq_repl (p):
  27       stream_eq_repl … (λf1,f2. ↑[p]f1 ≗ ↑[p]f2).
  28 #p elim p -p //
  29 * [ #k ] #p #IH #f1 #f2 #Hf
  30 [ /3 width=1 by stream_tls_eq_repl/
  31 | /2 width=1 by/
  32 | /3 width=1 by tr_push_eq_repl/
  33 | /2 width=1 by/
  34 | /2 width=1 by/
  35 ]
  36 qed.
  37
  38 lemma tls_lift_rmap_d_dx (f) (p) (n) (k):
  39       ⇂*[n+k]↑[p]f ≗ ⇂*[n]↑[p◖𝗱k]f.
  40 #f #p #n #k
  41 <lift_rmap_d_dx >nrplus_inj_dx >nrplus_inj_sn //
  42 qed.