Inductive Forallz {A} (P: Z -> A->Prop) : Z -> list A -> Prop :=
| Forallz_nil : forall i, Forallz P i nil
| Forallz_cons : forall i x l, P i x -> Forallz P (Z.succ i) l -> Forallz P i (x::l).
(******************************************  Definition of aggregate predicates.  ******************************************)
Definition array_pred {A: Type}{d: Inhabitant A}  (lo hi: Z) (P: Z -> A -> val -> mpred) (v: list A) (p: val) : mpred :=
!! (Zlength v = hi - lo) &&
rangespec lo (Z.to_nat (hi-lo)) (fun i => P i (Znth (i-lo) v)) p.
Definition struct_pred (m: members) {A: ident * type -> Type} (P: forall it, A it -> val -> mpred) (v: compact_prod (map A m)) (p: val): mpred.

Lemma split_array_pred: forall {A}{d: Inhabitant A} lo mid hi P v p,
lo <= mid <= hi ->
Zlength v = hi - lo ->
array_pred lo hi P v p =
array_pred lo mid P (sublist 0 (mid-lo) v) p *
array_pred mid hi P (sublist (mid-lo) (hi-lo) v) p.