 Finite representability of a Banach space

A Banach space $X$ is finitely representable in $Y$ when, for every finite-dimensional subspace $E\subseteq X$ and every $\epsilon >0$, there are a subspace $F\subseteq Y$ and an isomorphism $T:E\to F$ with $\Vert T\Vert \Vert T^{-1}\Vert <1+\epsilon$.