 The set of primitive recursive relations is also closed under bounded minimization. This is to say that if \(R(\vec{x},z)\) is a primitive recursive relation, then so is the function \(m_R(\vec{x},y)\) which returns the least \(z\) less than or equal to \(y\) such that \(R(\vec{x},z)\) holds if such a \(z\) exists and \(y+1\) otherwise—i.e., 