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_push_compat : forall i a S, Full S -> forall x, get i S = PSome x -> get i (push a S) = PSome x.