  In a recent paper, we showed that the large $(x,t)$ behavior of a class of
physically relevant solutions of Boussinesq's equation for water waves is
described by ten main asymptotic sectors. In the sector adjacent to the
positive $x$-axis, referred to as Sector I, we stated without proof an exact
expression for the leading asymptotic term together with an error estimate.
Here we provide a proof of this asymptotic formula.
