Given the following abstract data type:

fun {NewSet}

nil

end

fun {IsMember E X}

... %this Oz code is skipped, but you may assume this code is correct end

fun {Add E X}

X|E

end

Is the following definition a correct abstract data type?

fun {Extend E X}

if {IsMember E X} then E

else X|E

end

end

(Please answer in oz programming language)