  D.Happel and L.Unger defined a partial order on the set of basic tilting
modules. We study the poset of basic pre-projective tilting modules over path
algebra of infinite type. We give an equivalent condition for that this poset
is a distributive lattice. We also give an equivalent condition for that a
distributive lattice is isomorphic to the poset of basic pre-projective tilting
modules over a path algebra of representation infinite type.
