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Wegen $(u_i)_{i \in I}$ Basis von $U$, folgt also - $V / \text{ker}(\pi) \stackrel{\sim }{=} U$. + $V / \text{ker }(\pi) \stackrel{\sim }{=} U$. Damit: \[ \text{Bild}(\pi) \stackrel{\sim }{=} V / \text{ker }(\pi) \stackrel{\sim }{=} U - .\] Daraus folgt direkt: + .\] Da $U$ das Komplement zu $\text{ker }\pi$ ist, folgt + daraus direkt: \[ \text{Bild}(\pi) \oplus \text{ker }\pi \stackrel{\sim }{=} U \oplus \text{ker }\pi \stackrel{\sim }{=} V