Wikipedia
The derbfine (, ) was a term for patrilineal groups and power structures defined in the first written tracts in Early Irish law. Its principal purpose was as an institution of property inheritance, with property redistributed on the death of a member to those remaining members of the derbfine. Comprising all the patrilineal descendants over a four-generation group with a common great-grandfather, it gradually gave way to a smaller three-generation kinship group, called the gelfine.
Within a clan, on the death of its chief or king, the surviving members of its derbfine would elect from their number a new chief and/or elect his successor, or Tánaiste (in English, his Tanist). A larger number of clan members, either allies or cousins who were too distantly related to be members of the derbfine, would not have a direct say in such an election. The frequent recitations of a clan's genealogy by its bards was therefore a reminder of who was currently in or out of the clan's derbfine as much as it was a claim to ancient lineages.
Professor Francis John Byrne of University College Dublin also identified an indfine system used in some clans before the year 1000, with membership going back to a common great-great-great-grandfather, perhaps necessary at a time of frequent warfare.