The divergence obstruction for the two-variable reduction

Let $r(x)$ be a monic polynomial of degree $N+1>1$ with distinct roots, and let $\lambda(x)$ and $\mu(x)$ be the unique polynomials satisfying

$$r(x)\mu(x)+r'(x)\lambda(x)=1,$$

with $\deg\mu(x)\leq N-1$ and $\deg\lambda(x)\leq N$. Let

$$F_1(z_1,z_2)=r(z_1)H_1(z_1,z_2)-z_2\lambda(z_1)K_2(z_1,z_2),$$ $$F_2(z_1,z_2)=r(z_1)H_2(z_1,z_2)+z_2\lambda(z_1)K_1(z_1,z_2),$$

where $H_i$ and $K_i$ are polynomials satisfying $H_1K_1+H_2K_2=1$, and assume $F=(F_1,F_2)\in\mathcal F_1$. Let $A=a(z)\frac{\partial}{\partial z}$ be the formal differential operator associated with $F$. Divergence obstruction. Then

$$\triangledown A\neq 0.$$

The source says that, for this special class of two-variable polynomial maps, the Jacobian conjecture is equivalent to this assertion.