... (ar)t∈Tα,ni=1aγiyαγi≤t∈Tαatyαt. Furthermore, each Yαwill K-embed into Y .Just as in the proof of Theorem 7, it then follows from index theory that the Banach space spanned by (xi)∞i=1embeds ... , the Lipschitz distance dL(X, Y ) betweenthem is defined to be the infimum of Lip (f) · Lip (f−1), where the infimumis taken over all biLipschitz mappings f from X onto Y (the infimum of the empty ... complete the proof of Proposition 9, we assume that Y is K-elastic andprove that C[0, 1] embeds into Y . The proof is similar to, but simpler than, the proof of Theorem 7. First we recall the definition...