[FMFP] Restructure summary

semester4/fmfp/parts/01_induction-proofs/04_other-induction.tex

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+\subsection{Other types of induction}
+\subsubsection{Induction over Lists}
+To prove $P$ for all $xs$ in \texttt{[T]}, we do the following:
+
+\shade{blue}{Base case} We prove that $P[xs \mapsto []]$ is correct
+
+\shade{green}{Step case} We prove that $\forall y :: T, ys :: [T]. P[xs \mapsto ys] \rightarrow P[xs \mapsto y : ys]$, or in other words:
+We fix arbitrary $y :: T$ and $ys :: [T]$, which both are not free in $P$.
+We then apply our induction hypothesis $P[xs \mapsto ys]$ to prove $P[xs \mapsto y : ys]$
+
+