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\date{ }
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\begin{document}
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\maketitle
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\textbf{Referenzaufgabe:} \\
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%----------------------------------%
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\textbf{Referenzaufgabe:} \\
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\\
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\textbf{data List} a = $Nil$ $|$ $Cons$ a \textbf{List} a
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\begin{align*}
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snoc\;Nil\;a &= Cons\;a\;Nil
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snoc(Cons\;x\;xs)\;a &= Cons\;x(snoc\;xs\;a)
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snoc\;Nil\;a &= Cons\;a\;Nil\\
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snoc(Cons\;x\;xs)\;a &= Cons\;x\;(snoc\;xs\;a)
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\end{align*}
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\begin{align*}
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Nil + ys &= ys\\
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(Cons\;x\;xs) + ys &= Cons\;x\;(xs + ys)
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\end{align*}
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\underline{Beweisen sie dass:}\\
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$\forall e,\;xs,\;ys\\xs+(Cons\;e\;ys) = (snoc\;xs\;e)+ys$ \\\\
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%----------------------------------%
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\textbf{Induktionsanfang:}\\\\
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$xs = Nil$\;\;$\Rightarrow$ Einsetzen und beide Seiten maximal vereinfachen
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\begin{align*}
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Nil+(Cons\;e\;ys) &= (snoc\;Nil\;e)+ys\\
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Cons\;e\;ys &= (snoc\;Nil\;e)+ys\\
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Cons\;e\;ys &= (Cons e Nil) + ys\\
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Cons\;e\;ys &= Cons\;e (Nil + ys)\\
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Cons\;e\;ys &= Cons\;e\;ys
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\end{align*}
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\begin{tiny}
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\copyright\ Joint-Troll-Expert-Group (JTEG) 2015
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\end{tiny}
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