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

Theorem get_Full_Gt : forall S, Full S -> forall i, (i ?= index S) = Gt -> get i S = PNone.