And the ruling is like Abayay in Ya’AhL KaGaM - והילכתא כוותיה דאביי ביע"ל קג"ם
The ר"ת (initially) maintains that if there were שידוכין or a verbal agreement (or even if there was no agreement) she is מקודשת to the intended (or to the oldest). While הר"ר מנחם מיוני disagrees and in all cases they all require a גט even by שידך.
And even in a situation where she becomes her rival - ואפילו במקום שנעשית לה צרה
The חידוש of רב is either that we are not concerned that she wishes to ruin her צרה (since there was a מעשה), or that we assume that she accepted her שליחות even if she did not say so explicitly.