 Now to show \(\forall x(R^{+}(a,x) \to Px)\), pick an arbitrary object, say \(b\), and further assume \(R^{+}(a,b)\). We then simply have to show \(Pb\). We do this by invoking Fact (7) about \(R^{+}\) (in our subsection on the Weak Ancestral in §4). Recall that Fact (7) is: 