matita/matita/contribs/lambdadelta/ground/relocation/tr_pap.ma

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  14
  15 include "ground/notation/functions/atsharp_2.ma".
  16 include "ground/arith/pnat_plus.ma".
  17 include "ground/relocation/tr_map.ma".
  18
  19 (* POSITIVE APPLICATION FOR TOTAL RELOCATION MAPS ***************************)
  20
  21 (*** apply *)
  22 rec definition tr_pap (i: pnat) on i: tr_map → pnat.
  23 * #p #f cases i -i
  24 [ @p
  25 | #i lapply (tr_pap i f) -tr_pap -i -f
  26   #i @(i+p)
  27 ]
  28 defined.
  29
  30 interpretation
  31   "functional positive application (total relocation maps)"
  32   'AtSharp f i = (tr_pap i f).
  33
  34 (* Basic constructions ******************************************************)
  35
  36 (*** apply_O1 *)
  37 lemma tr_cons_pap_unit (f):
  38       ∀p. p = (p⨮f)＠⧣❨𝟏❩.
  39 // qed.
  40
  41 (*** apply_S1 *)
  42 lemma tr_cons_pap_succ (f):
  43       ∀p,i. f＠⧣❨i❩+p = (p⨮f)＠⧣❨↑i❩.
  44 // qed.