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experiments
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davidcok committed Jul 2, 2020
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Expand Up @@ -2743,10 +2743,10 @@ that the recursive _depth_ in evaluating $f$
on any given argument is finite. That is, there are no infinite descending chains
of recursive calls. However, the evaluation of $f$ on a given argument
may fail to terminate, because its _width_ may be infinite. For example, let $P$
be some predicate defined on the ordinals and let $\mathit{PDownward}$ be a predicate on the
be some predicate defined on the ordinals and let $\mathit{P}\downarrow$ be a predicate on the
ordinals defined by the following equation:

\\[\mathit{PDownward}(o) = P(o) \;\wedge\; \forall p \bullet\; p \ll o \;\Longrightarrow\; \mathit{PDownward}(p\\]
\\[\mathit{P}\downarrowo) = P(o) \;\wedge\; \forall p \bullet\; p \ll o \;\Longrightarrow\; \mathit{P}\downarrow(p\\]


With $\ll$ as the usual ordering on ordinals, this equation satisfies the decrement
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