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Theorem frag-split

⊦ ¬ # α < ⌜n⌝ ∧ ⌜n⌝ < # σ → ( frag(IOAut(start, step, ext))(σ, α) ↔ frag*(IOAut(start, step, ext))(σ.take(n + 1), α.take(n)) ∧ frag(IOAut(start, step, ext))(σ.drop(n), α.drop(n)))

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