,y,z,u^0,a,\nu)&\leq \int_{E}\delta^{0,0} u(x)\gamma_t(x)\nu(dx),\end{aligned}$$ where $\delta^{0,0} u:=u^0-u^0$ and $c_0(0\wedge {\left|x\right|}) \leq \gamma_t(x) \leq c_0(0\wedge {\left|x\right|})$ with $-0+\delta\leq c_0\leq0, \; c_0\geq 0,$ and $c_0'(0\wedge {\left|x\right|}) \leq \gamma'_t(x) \leq c_0'(0\wedge {\left|x\right|})$ with $-0+\delta\leq c_0'\leq0, \; c_0'\geq 0,$ for some $\delta >0$.  [(v)]{} $F$ is uniformly continuous in $\omega$ for the Skorohod topology, that is to say that there exists some modulus of continuity $\rho$ such that for all $(t,