Fixpoint In (x:A) (S:Store) (F:Full S) {struct F}: Prop :=
match F with
F_empty => False
| F_push a SS FF => x=a \/ In x SS FF
end.

(* Specifications: *)
Lemma get_In : forall (x:A) (S:Store) (F:Full S) i , get i S = PSome x -> In x S F.