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Typo fixes in Chapter 2

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Adam Chlipala 2017-02-07 14:49:38 -05:00
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frap_book.tex
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@ -46,7 +46,7 @@ For more information, see the book's home page:
\mbox{}\vfill \mbox{}\vfill
\begin{center} \begin{center}
Copyright Adam Chlipala 2015-2016. Copyright Adam Chlipala 2015-2017.
This work is licensed under a This work is licensed under a
@ -293,7 +293,7 @@ To derive an $\mathsf{Exp}$ structural induction principle, we produce a new set
\item For each premise $E \in S$, add a companion premise $P(E)$. That is, the obligation allows \emph{assuming} that $P$ holds of certain terms. Each such assumption is called an \emph{inductive hypothesis}\index{inductive hypothesis} (\emph{IH}\index{IH}). \item For each premise $E \in S$, add a companion premise $P(E)$. That is, the obligation allows \emph{assuming} that $P$ holds of certain terms. Each such assumption is called an \emph{inductive hypothesis}\index{inductive hypothesis} (\emph{IH}\index{IH}).
\end{enumerate} \end{enumerate}
That mechanical procedure derives the following four proof obligations, associated with an inductive proof that $\forall x \in \mathsf{X}. \; P(x)$. That mechanical procedure derives the following four proof obligations, associated with an inductive proof that $\forall x \in \mathsf{Exp}. \; P(x)$.
$$\infer{P(\mathsf{Const}(n))}{ $$\infer{P(\mathsf{Const}(n))}{
n \in \mathbb N n \in \mathbb N
} }
@ -313,7 +313,7 @@ $$\quad \infer{P(\mathsf{Plus}(e_1, e_2))}{
& P(e_2) & P(e_2)
}$$ }$$
In other words, to establish $\forall x \in \mathsf{X}. \; P(x)$, we need to prove that each of these inference rules is valid. In other words, to establish $\forall x \in \mathsf{Exp}. \; P(x)$, we need to prove that each of these inference rules is valid.
To see induction in action, we prove a theorem giving a sanity check on our two recursive definitions from earlier: depth can never exceed size. To see induction in action, we prove a theorem giving a sanity check on our two recursive definitions from earlier: depth can never exceed size.
\begin{theorem} \begin{theorem}