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@@ -174,7 +174,7 @@
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\end{itemize}
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In which case, since $U_{k} \supset U_{k+1}$ for all $k \in \natp$,
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\[
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\underbracs{y - \sum_{k = 1}^n \lambda_kx_k}_{\in E_n} = \underbrace{z + \sum_{k = n + 1}^N \lambda_kx_k}_{\in F_n + U_n}
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\underbrace{y - \sum_{k = 1}^n \lambda_kx_k}_{\in E_n} = \underbrace{z + \sum_{k = n + 1}^N \lambda_kx_k}_{\in F_n + U_n}
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\]
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which is impossible. Therefore $(F_n + U) \cap E_n = \emptyset$ for all $n \in \natp$.
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