The intermediate value conjecture for hyperseries

Let $\textbf{Hy}$ be the intended field of hyperseries, equipped with field operations, differentiation, and composition. Let $\Phi$ be a partial function from $\textbf{Hy}$ into itself constructed from elements of $\textbf{Hy}$ using those operations. Intermediate value conjecture for hyperseries. If $f<g$ are hyperseries in $\textbf{Hy}$, $\Phi$ is defined on the closed interval $[f,g]$, and

$$\Phi(f)\Phi(g)<0,$$

then there exists $y\in\textbf{Hy}$ such that

$$\Phi(y)=0\quad\text{and}\quad f<y<g.$$

The claim seeks an intermediate-value property for functions generated using differentiation and composition in the proposed hyperseries field; the source gives no resolution.