diff --git a/src/fa/lc/inductive.tex b/src/fa/lc/inductive.tex index 072544f..1643234 100644 --- a/src/fa/lc/inductive.tex +++ b/src/fa/lc/inductive.tex @@ -174,7 +174,7 @@ \end{itemize} In which case, since $U_{k} \supset U_{k+1}$ for all $k \in \natp$, \[ - \underbracs{y - \sum_{k = 1}^n \lambda_kx_k}_{\in E_n} = \underbrace{z + \sum_{k = n + 1}^N \lambda_kx_k}_{\in F_n + U_n} + \underbrace{y - \sum_{k = 1}^n \lambda_kx_k}_{\in E_n} = \underbrace{z + \sum_{k = n + 1}^N \lambda_kx_k}_{\in F_n + U_n} \] which is impossible. Therefore $(F_n + U) \cap E_n = \emptyset$ for all $n \in \natp$.