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$\mathbb {E}$ FROM 
$\mathbb {E}\upharpoonright \aleph _1$ IN 
$L[\mathbb {E}]$
Let M be a short extender mouse. We prove that if 
$E\in M$ and 
$M\models $“E is a countably complete short extender whose support is a cardinal 
$\theta $ and 
$\mathcal {H}_\theta \subseteq \mathrm {Ult}(V,E)$”, then E is in the extender sequence 
$\mathbb {E}^M$ of M. We also prove other related facts, and use them to establish that if 
$\kappa $ is an uncountable cardinal of M and 
$\kappa ^{+M}$ exists in M then 
$(\mathcal {H}_{\kappa ^+})^M$ satisfies the Axiom of Global Choice. We prove that if M satisfies the Power Set Axiom then 
$\mathbb {E}^M$ is definable over the universe of M from the parameter 
$X=\mathbb {E}^M\!\upharpoonright \!\aleph _1^M$, and M satisfies “Every set is 
$\mathrm {OD}_{\{X\}}$”. We also prove various local versions of this fact in which M has a largest cardinal, and a version for generic extensions of M. As a consequence, for example, the minimal proper class mouse with a Woodin limit of Woodin cardinals models “
$V=\mathrm {HOD}$”. This adapts to many other similar examples. We also describe a simplified approach to Mitchell–Steel fine structure, which does away with the parameters 
$u_n$.
