MAYBE

Problem:
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(treemap(),f),app(app(node(),x),xs)) ->
 app(app(node(),app(f,x)),app(app(map(),app(treemap(),f)),xs))

Proof:
 Open