[see also: importance, significance, relevance, interest
By interchanging <exchanging> 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 <principal/significant/important> role