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Typo fixes in Chapter 2
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@ -46,7 +46,7 @@ For more information, see the book's home page:
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\mbox{}\vfill
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\mbox{}\vfill
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\begin{center}
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\begin{center}
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Copyright Adam Chlipala 2015-2016.
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Copyright Adam Chlipala 2015-2017.
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This work is licensed under a
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This work is licensed under a
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@ -293,7 +293,7 @@ To derive an $\mathsf{Exp}$ structural induction principle, we produce a new set
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\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}).
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\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}).
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\end{enumerate}
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\end{enumerate}
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That mechanical procedure derives the following four proof obligations, associated with an inductive proof that $\forall x \in \mathsf{X}. \; P(x)$.
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That mechanical procedure derives the following four proof obligations, associated with an inductive proof that $\forall x \in \mathsf{Exp}. \; P(x)$.
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$$\infer{P(\mathsf{Const}(n))}{
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$$\infer{P(\mathsf{Const}(n))}{
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n \in \mathbb N
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n \in \mathbb N
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}
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}
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@ -313,7 +313,7 @@ $$\quad \infer{P(\mathsf{Plus}(e_1, e_2))}{
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& P(e_2)
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& P(e_2)
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}$$
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}$$
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In other words, to establish $\forall x \in \mathsf{X}. \; P(x)$, we need to prove that each of these inference rules is valid.
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In other words, to establish $\forall x \in \mathsf{Exp}. \; P(x)$, we need to prove that each of these inference rules is valid.
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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.
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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.
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\begin{theorem}
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\begin{theorem}
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