IF: Beside CV or maybe employment contracts, how can researchers prove that they have more than 4 years of full-time equivalent research experience?

An employment contract that specifically mentions research as one of the researcher’s job responsibilities is the best evidence of FTE research experience. If they have been registered as a research student without employment contract (as is the case for all doctoral candidates in Ireland), then a copy of the student registration or an official letter from the university where they are studying would be good instead.