 TS-indep:  \(M \models_X \vec x \mathop{\bot_{\vec z}} \vec y\) if and only if for all \(s, s' \in X\) with \(s(\vec z) = s'(\vec z)\) there exists a \(s'' \in X\) with \(s''(\vec z\, \vec x) = s(\vec{x}\, \vec{z})\) and \(s''(\vec y) = s'(\vec y)\).