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).

Lemma Full_index_one_empty : forall S, Full S -> index S = 1 -> S=empty.