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