Proposition
50
[1XS] Assume that a (partial) order associated to \(β\) satisfies [26H]. Let \(P(n)\) be a logical clause, true for \(n=0\) and such that
\begin{equation} β nβ β , \Big( \big(β kβ€ n, P(k)\big)β P(Sn)\Big)\label{eq:passo_ induttivo_ forte} \end{equation}
51
then \(P\) is true for every \(nββ\).