(******************************************

Definitions of spacer and withspacer

Comment: spacer only has offset_zero property but does not have local_facts
and isptr property.

******************************************)

Definition spacer (sh: share) (be: Z) (ed: Z) : val -> mpred :=
  if Z.eq_dec (ed - be) 0
  then fun _ => emp
  else
    at_offset (memory_block sh (ed - be)) be.(* Arguments spacer sh be ed / _ . *)

Definition withspacer sh (be: Z) (ed: Z) P (p: val): mpred :=
   if Z.eq_dec (ed - be) 0
   then P p
   else P p * spacer sh be ed p.

Lemma withspacer_add: forall sh pos be ed P p, withspacer sh (pos + be) (pos + ed) (fun p0 => P (offset_val pos p)) p = withspacer sh be ed P (offset_val pos p).