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13 lines
1.3 KiB
TeX
13 lines
1.3 KiB
TeX
\subsection{Workflow}
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{\scriptsize the notes in this section may seem a bit over the top,
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but in the exercise sessions it was mentioned repeatedly that they will heavily deduct points for not following the scheme.
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One example that was named is that in some exams out of 36 points for a proof, 9 were awarded for simply following the expected structure}
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\begin{enumerate}
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\item Determine the exact expression to proof (possibly generalizing it, and if so, state something like ``Consider the generalized statement'')
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\item Then, start the proof by stating something along the lines of ``We prove $\forall n \in \N P$ by weak mathematical induction on $n$''.
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\item Depending on the proof type, proceed with base cases, or case analysis. \hl{Important}: State ``Let $m$ be arbitrary'' for free variables,
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and if there are extra variables introduced by the application (e.g. a \texttt{Leaf} type has value $x$ in it), state ``Fix $x$ and we show $P[t \mapsto \texttt{Leaf} x]$''
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\item Then, do the step case (if applicable). \hl{Important}: State ``Let $n$ be arbitrary'', or in the case of structural induction, there may be arguments for the type,
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such as for \texttt{Tree}, then state ``Let \texttt{l::Tree} and \texttt{r::Tree} be arbitrary''.
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\end{enumerate}
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