[see also: part, importance, significance, relevance, interest]

By interchanging $\langle$exchanging$\rangle$ the roles of $X$ and $Y$, it follows that ......

Here $f$ takes over the role of the time parameter.

It turns out that these properties play no role in the proof.

In closing this section we take up a result which will play a pivotal role in the characterization of ......

Its role is to rule out having two or more consecutive $P$-moves (on the grounds that they can be performed in one go).

a key $\langle$principal/significant/important$\rangle$ role

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