Pushing is particularly interesting in the case of join, because there are multiple inputs. Generally an expression can be pushed down to a particular input if it depends upon no other inputs. If it can be pushed down to both sides, it is pushed down to the left.
Sometimes an expression needs to be split before it can be pushed down. To flag that an expression cannot be split, specify a rule that it must be preserved. Such an expression will be pushed down intact to one of the inputs, or not pushed down at all.
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