  We prove that asymptotic global consensus is always reached in the
Hegselmann-Krause model with finite speed of information propagation
$\mathfrak{c}>0$ under minimal (i.e., necessary) assumptions on the influence
function. In particular, we assume that the influence function is globally
positive, which is necessary for reaching global consensus, and such that the
agents move with speeds strictly less than $\mathfrak{c}$, which is necessary
for well-posedness of solutions. From this point of view, our result is
optimal. The proof is based on the fact that the state-dependent delay, induced
by the finite speed of information propagation, is uniformly bounded.
