Final answer:
EFI stands for Expected Future Inbreeding and is used in animal breeding to estimate the potential increase in inbreeding over future generations.
Step-by-step explanation:
In regards to published bull proofs, the initials EFI stand for Expected Future Inbreeding. EFI is a measure used in animal breeding to estimate the potential increase in inbreeding over future generations. It helps breeders make informed decisions to avoid excessive levels of inbreeding, which can lead to reduced fertility and health problems in animals.