Qed.
Inductive Full : Store -> Type:=
F_empty : Full empty
| F_push : forall a S, Full S -> Full (push a S).

(* Specifications: *)
Theorem get_Full_Gt : forall S, Full S ->
forall i, (i ?= index S) = Gt -> get i S = PNone.
Theorem get_Full_Eq : forall S, Full S -> get (index S) S = PNone.
intros [index0 contents0] F.