# Return the set of all elements `f` that have an edge from `f` to `element`.
	#
	# ~~~~
	# var pos = new POSet[String]
	# pos.add_chain(["A", "B", "C", "D"])
	# assert pos["C"].direct_smallers.has_exactly(["B"])
	# ~~~~
	fun direct_smallers: Collection[E]
	do
		return self.dfroms
	end