matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap.etc

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  14
  15 include "ground/arith/pnat_plus.ma".
  16 include "ground/relocation/tr_map.ma".
  17 include "delayed_updating/notation/functions/verticalbarat_2.ma".
  18
  19 (* POSITIVE APPLICATION FOR STACKS OF BASIC RELOCATION MAPS *****************)
  20
  21 rec definition sbr_pap (i: pnat) on i: tr_map → pnat.
  22 * #p #f cases i -i
  23 [ @(p)
  24 | #i cases p -p
  25   [ lapply (sbr_pap i f) -sbr_pap -i -f
  26     #i @(↑i)
  27   | #p @(i+↑p)
  28   ]
  29 ]
  30 defined.
  31
  32 interpretation
  33   "functional positive application (stack of relocation maps)"
  34   'VerticalBarAt f i = (sbr_pap i f).
  35
  36 (* Basic constructions ******************************************************)
  37
  38 lemma sbr_pap_unfold_unit (f):
  39       ∀p. p = (p⨮f)❘@❨𝟏❩.
  40 // qed.
  41
  42 lemma sbr_pap_unfold_unit_succ (f):
  43       ∀i. ↑(f❘@❨i❩) = (𝟏⨮f)❘@❨↑i❩.
  44 // qed.
  45
  46 lemma sbr_pap_unfold_succ_bi (f):
  47       ∀p,i. i+↑p = (↑p⨮f)❘@❨↑i❩.
  48 // qed.