  We present a method for establishing invariant manifolds for saddle--center
fixed points. The method is based on cone conditions, suitably formulated to
allow for application in computer assisted proofs, and does not require
rigorous integration of the vector field in order to prove the existence of the
invariant manifolds. We apply our method to the restricted three body problem
and show that for a given choice of the mass parameter, there exists a
homoclinic orbit to one of the libration points.
