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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "ground/notation/functions/atsharp_2.ma".
16 include "ground/arith/pnat_plus.ma".
17 include "ground/relocation/tr_map.ma".
19 (* POSITIVE APPLICATION FOR TOTAL RELOCATION MAPS ***************************)
22 rec definition tr_pap (i: pnat) on i: tr_map → pnat.
25 | #i lapply (tr_pap i f) -tr_pap -i -f
31 "functional positive application (total relocation maps)"
32 'AtSharp f i = (tr_pap i f).
34 (* Basic constructions ******************************************************)
37 lemma tr_cons_pap_unit (f):
42 lemma tr_cons_pap_succ (f):
43 ∀p,i. f@⧣❨i❩+p = (p⨮f)@⧣❨↑i❩.