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@ -134,7 +134,7 @@ Applications of induction and recursion:
on a class $A$. on a class $A$.
Then there is a function $F\colon A \to \OR$, Then there is a function $F\colon A \to \OR$,
such that for all $x,y \in A$ such that for all $x,y \in A$
\[(x,y) \in R \implies F(x) < F(y).\] \[(x,y) \in R \implies F(x) < F(y) F(x) < F(y).\]
\end{lemma} \end{lemma}
\begin{proof} \begin{proof}
By the recursion theorem, By the recursion theorem,