Fresh renaming

Given a set of variables $\begin{array}{l}\\ mathcalX\end{array}$ and a finite sequence of variables $\begin{array}{l}\\ vecx\end{array}$, a bijection $\begin{array}{l}\\ rho:\\ vecx\\ leftrightarrow\\ vec{x}^{\prime }\end{array}$ between $\begin{array}{l}\\ vecx\end{array}$ and $\begin{array}{l}\\ vec{x}^{\prime }\end{array}$, where $\begin{array}{l}\\ vec{x}^{\prime }\end{array}$ is fresh f

Given a set of variables $𝒳$ and a finite sequence of variables $\overrightarrow{x}$, a bijection $\rho :\overrightarrow{x}\leftrightarrow {\overrightarrow{x}}^{\prime }$ between $\overrightarrow{x}$ and ${\overrightarrow{x}}^{\prime }$, where ${\overrightarrow{x}}^{\prime }$ is fresh for $𝒳$.