  In this paper, we study some variations of Namba forcing
$\mathrm{Nm}(\kappa,\lambda)$ over $\mathcal{P}_{\kappa}\lambda$ and show that
its semiproperness implies $\mathrm{SSR}([\lambda]^{\omega},{<}\kappa)$.
  In particular, Prikry forcing at $\mu$ forces Namba forcing
$\mathrm{Nm}(\mu^{+})$ is not semiproper. This shows that there is no
semiproper saturated ideal in the extensions by Prikry-type forcings. We also
show that $[\lambda^{+}]^{\mu^{+}}$ cannot carry a $\lambda^{+}$-saturated
semiproper ideal if $\mu$ is singular with countable cofinality.
