Both-vertical non-associated pair has intersection below any bound

Let $h$ and $k$ be irreducible bivariate real polynomials ($h_h$, $h_k$) that are not associated ($h_{not}$), and suppose both are vertical: $h_{deg0} : (\mathrm{Curry0}\,h).\mathrm{natDegree} = 0$ and $k_{deg0} : (\mathrm{Curry0}\,k).\mathrm{natDegree} = 0$. Then for every natural number $B$ (an arbitrary bound parameter) the intersection is finite and bounded by $B$:

Since each curve is a union of vertical lines and the two line families are disjoint (a shared line would make the irreducibles associated), the intersection is actually empty, hence below any $B$. This vacuous-but-uniform case closes the both-vertical branch of the irreducible pair-intersection case split with a bound that composes with the other branches.