  We revisit the evaluation of the pionic mechanism of the
$\bar{u}-\bar{d}$-asymmetry in the proton structure function. Our analysis is
based on the extended AGK unitarity relation between contributions of different
mechanisms to the inclusive particle production and the total photoabsorption
cross-section (i.e. the proton structure function). We reanalyze the role of
isovector reggeons in inclusive production of nucleons and Delta isobars in
hadronic reactions. We find rather large contribution of reggeon-exchange
induced production of Delta isobars. This leaves much less room for the
pion-exchange induced mechanism of $\Delta$ production and provides a
constraint on the $\pi N \Delta$ form factor. The production of leading pions
in proton-proton collisions at ISR puts additional constraints on the $\pi NN$
vertex form factors. An extension of the AGK-rules to reggeon exchange suggests
a negligible contribution to the proton structure function from DIS off the
exchanged $\rho,a_2$ reggeons. All these constraints are used then to estimate
the pion content of the nucleon and allow to calculate parameter-free the
$x$-dependence of $\bar d - \bar u$. We discuss the violation of the Gottfried
Sum Rule and $\bar d$-$\bar u$ asymmetry and compare to the one obtained from
the E866 experiment at Fermilab. We estimate the background to the pion
structure function being determined by the ZEUS and H1 collaborations at HERA
from leading neutron experiments.
