[see also: when, whenever, whether, provided]
The map $F$ is said to be proper if $G$ is dense. [ Note: no comma before if here.]
By deleting the intervals containing $x$, if any, we obtain ......
There are few, if any, other significant classes of processes for which such precise information is available.
The only thing to check is that maps compose correctly; but this is an easy, if tedious, verification.
We can assume, by decreasing $n$ if necessary, that ......
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