 It is worth pointing out here that it is not in general required by the above definition that \(X\) and \(Y\) contain the same number of assignments: a single assignment in \(X\) may well correspond to multiple assignments in \(Y\), and—if \(v\) is already a variable occurring in the assignments of \(X\)—a single assignment in \(Y\) may also correspond to multiple assignments in \(X\).