  $SRA$-free spaces is a wide class of metric spaces including finite
dimensional Alexandrov spaces of non-negative curvature, complete Berwald
spaces of nonnegative flag curvature, Cayley Graphs of virtually abelian groups
and doubling metric spaces of non-positive Busemann curvature with extendable
geodesics. This class also includes arbitrary big balls in complete, locally
compact $CAT(k)$-spaces $(k \in \mathbb R)$ with locally extendable geodesics,
finite-dimensional Alexandrov spaces of curvature $\ge k$ with $k \in R$ and
complete Finsler manifolds satisfying the doubling condition.
  We show that $SRA$-free spaces allow bi-Lipschitz embeddings in Euclidean
spaces. As a corollary we obtain a quantitative bi-Lipschitz embedding theorem
for balls in finite dimensional Alexandrov spaces of curvature bounded from
below conjectured by S. Eriksson-Bique.
  The main tool of the proof is an extension theorem for bi-Lipschitz maps into
Euclidean spaces. This extension theorem is close in nature with the embedding
theorem of J. Seo and may be of independent interest.
