(******************************************  Definitions of spacer and withspacer  Comment: spacer only has offset_zero property but does not have local_facts and isptr property.  ******************************************)
(* 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 spacer_sepcon_memory_block: forall sh ofs lo hi b i,
0 <= lo ->
0 <= ofs ->
lo <= hi < Ptrofs.modulus ->
Ptrofs.unsigned i + ofs + hi < Ptrofs.modulus ->
spacer sh (ofs + lo) (ofs + hi) (Vptr b i) * memory_block sh lo (offset_val ofs (Vptr b i)) = memory_block sh hi (offset_val ofs (Vptr b i)).