 In other words, \(F\) is hereditary on the members of the \(R\)-series beginning with \(a\) just in case every adjacent pair \(x\) and \(y\) in this series (with \(x\) bearing \(R\) to \(y\)) is such that \(y\) falls under \(F\) whenever \(x\) falls under \(F\). Now given this definition, we can reformulate the General Principle of Induction more strictly as: 