The OPERA experiment is searching for nu_mu -> nu_tau oscillations in
appearance mode i.e. via the direct detection of tau leptons in nu_tau charged
current interactions. The evidence of nu_mu -> nu_tau appearance has been
previously reported with three nu_tau candidate events using a sub-sample of
data from the 2008-2012 runs. We report here a fourth nu_tau candidate event,
with the tau decaying into a hadron, found after adding the 2012 run events
without any muon in the final state to the data sample. Given the number of
analysed events and the low background, nu_mu -> nu_tau oscillations are
established with a significance of 4.2sigma.Comment: Submitted to Progress of Theoretical and Experimental Physics (PTEP