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\section{Aritmetick\'{e} priestory $\mathbf{R}^{n}$ a $\mathbf{C}^{n}$}
\subsection{D\^{o}kaz vety}
(sporom)
Keby boli $\mathbf{x}_{1},\,\mathbf{x}_{2},\,\ldots ,\,\mathbf{x}_{k}$ line%
\'{a}rne z\'{a}visl\'{e}, potom pod\v{l}a predo\v{s}lej vety by boli aj $%
\mathbf{x}_{1},\,\mathbf{x}_{2},\,\ldots ,\,\mathbf{x}_{m}$ line\'{a}rne z%
\'{a}visl\'{e}, \v{c}o je spor s predpokladom vety. $\blacksquare $
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