FlyerTalk Evangelist
Join Date: Feb 2009
Location: From ORK, live LCY
Programs: BA Silver, EI Silver, HH Gold, BW Gold, ABP, Seigneur des Horaires des Mucci
Posts: 14,244
Unless you left Ireland overland or on a local journey within the common travel area, you would have provided your passport details of your departing journey to your carrier who will have transmitted them to the Irish government.
If this somehow wasn't recorded, you can also use your boarding pass, frequent flyer history, stamps at subsequent destinations, or other evidence to show you left in good time.