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\[
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\[
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\forall x \in X.~(\exists n.~(x,n) \in R \iff \exists! n.~(x,n)\in R^\ast).
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\forall x \in X.~(\exists n.~(x,n) \in R \iff \exists! n.~(x,n)\in R^\ast).
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\]
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\]
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We say that $R^\ast$ \vocab[uniformization]{uniformizes} $R$.
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We say that $R^\ast$ \vocab[uniformization]{uniformizes} $R$.%
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\todo{missing picture
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\footnote{Wikimedia has a \href{https://upload.wikimedia.org/wikipedia/commons/4/4c/Uniformization_ill.png}{nice picture.}}
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\url{https://upload.wikimedia.org/wikipedia/commons/4/4c/Uniformization_ill.png}}
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\end{theorem}
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\end{theorem}
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\begin{proof}
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\begin{proof}
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