  We show that (i) the standard fine structural properties for premice follow
from normal iterability (whereas the classical proof relies on iterability for
stacks of normal trees), and (ii) every mouse which is finitely generated above
its projectum, is an iterate of its core.
  That is, let $m$ be an integer and let $M$ be an $m$-sound,
$(m,\omega_1+1)$-iterable premouse. Then (i) $M$ is $(m+1)$-solid and
$(m+1)$-universal, $(m+1)$ condensation holds for $M$, and if $m\geq 1$ then
$M$ is super-Dodd-sound, a slight strengthening of Dodd-soundness. And (ii) if
there is $x\in M$ such that $M$ is the $\mathrm{r}\Sigma_{m+1}$-hull of
parameters in $\rho_{m+1}^M\cup\{x\}$, then $M$ is a normal iterate of its
$(m+1)$-core $C=\mathfrak{C}_{m+1}(M)$; in fact, there is an $m$-maximal
iteration tree $\mathcal{T}$ on $C$, of finite length, such that
$M=M^{\mathcal{T}}_\infty$, and $i^{\mathcal{T}}_{0\infty}$ is just the core
embedding.
  Applying fact (ii), we prove that if $M\models\mathrm{ZFC}$ is a mouse and
$W\subseteq M$ is a ground of $M$ via a strategically $\sigma$-closed forcing
$\mathbb{P}\in W$, and if $M|\aleph_1^M\in W$ (that is, the initial segment of
$M$ of height $\aleph_1^M$ is in $W$), then the forcing is trivial; that is,
$M\subseteq W$.
  And if there is a measurable cardinal, then there is a non-solid premouse.
  The results hold for premice with Mitchell-Steel indexing, allowing extenders
of superstrong type to appear on the extender sequence.
