  We give a new proof of a theorem of Kleiner-Leeb: that any
quasi-isometrically embedded Euclidean space in a product of symmetric spaces
and Euclidean buildings is contained in a metric neighborhood of finitely many
flats, as long as the rank of the Euclidean space is not less than the rank of
the target. A bound on the size of the neighborhood and on the number of flats
is determined by the size of the quasi-isometry constants.
  Without using asymptotic cones, our proof focuses on the intrinsic geometry
of symmetric spaces and Euclidean buildings by extending the proof of
Eskin-Farb's quasiflat with holes theorem for symmetric spaces with no
Euclidean factors.
