Simplicity of the roots generated by the Newton sequence

Let $Y_{n,m}(t)$ be the sequence of functions used to generate the approximations, and define

$$y_n=\lim_{m\rightarrow\infty}Y_{n,m}(t).$$

The roots generated by this sequence are the zeros $y_n$ of the corresponding function. Simplicity conjecture. The roots generated by the sequence $y_n=\lim_{m\rightarrow\infty}Y_{n,m}(t)$ are simple. The surrounding discussion relates simplicity to super-attractive fixed points of the Newton map, but no resolution of this conjecture is supplied.