  Let X and Y be two infinite-dimensional Banach spaces. If X is crudely
finitely representable in every finite-codimensional subspace of Y, then any
proper subset of X almost bi-Lipschitz embeds into Y, in a sense quite close to
that of F. Baudier and G. Lancien. This is an extension of a result proved by
M.I. Ostrovskii for locally finite subsets.

Functional Analysis