Removable singularities for quasiregular mappings

Given a continuous open finite-to-one mapping $f$ of a domain $G$ including a closed set $E$, for each natural $k$ we consider the set $E(k)$ (possibly empty) of all points in $E$ at which $f$ attains a value with multiplicity $k$ over $G$. Suppose that each point of $E(k)$ has a neighborhood where the restriction of $f$ to $E(k)$ is injective, and its inverse mapping is weakly $(h,H)$-quasisymmetric. If, moreover, $f$ is quasiregular outside $E$, then it is quasiregular on the entire domain $G$. This theorem generalizes the sufficient condition for the removability of closed sets in the class of quasiconformal mappings obtained by Väisälä in 1990.