On some notions of good reduction for endomorphisms of the projective line

Let $\mathrm{\Phi }$ be an endomorphism of $\text{SR}(\bar{\text{Q}})$, the projective line over the algebraic closure of $\text{Q}$, of degree $\ge 2$ defined over a number field $K$. Let $v$ be a non-archimedean valuation of $K$. We say that $\mathrm{\Phi }$ has critically good reduction at $v$ if any pair of distinct ramification points of $\mathrm{\Phi }$ do not collide under reduction modulo $v$ and the same holds for any pair of branch points. We say that $\mathrm{\Phi }$ has simple good reduction at $v$ if the map ${\mathrm{\Phi }}_v$, the reduction of $\mathrm{\Phi }$ modulo $v$, has the same degree of $\mathrm{\Phi }$. We prove that if $\mathrm{\Phi }$ has critically good reduction at $v$ and the reduction map ${\mathrm{\Phi }}_v$ is separable, then $\mathrm{\Phi }$ has simple good reduction at $v$.