Hint Rewrite mapsto_force_ptr: norm.
(******************************************  Definition of at_offset.  at_offset is the elementary definition. All useful lemmas about at_offset will be proved here.  ******************************************)
Definition at_offset (P: val -> mpred) (z: Z): val -> mpred :=
fun v => P (offset_val z v).
Arguments at_offset P z v : simpl never.

Lemma at_offset_derives: forall P Q p , (forall p, P p |-- Q p) -> forall pos, at_offset P pos p |-- at_offset Q pos p.
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.