Added [simp]-lemmas "in_inv_image" and "in_lex_prod" in the spirit of "in_measure".
This simplifies some proofs.
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\begin{isabellebody}%
\def\isabellecontext{fakenat}%
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\isadelimtheory
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\endisadelimtheory
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\isatagtheory
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\endisatagtheory
{\isafoldtheory}%
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\isadelimtheory
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\endisadelimtheory
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\begin{isamarkuptext}%
\noindent
The type \tydx{nat} of natural
numbers is predefined to have the constructors \cdx{0} and~\cdx{Suc}. It behaves as if it were declared like this:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
\ nat\ {\isacharequal}\ {\isadigit{0}}\ {\isacharbar}\ Suc\ nat%
\isadelimtheory
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\endisadelimtheory
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\isatagtheory
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\endisatagtheory
{\isafoldtheory}%
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\isadelimtheory
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\endisadelimtheory
\end{isabellebody}%
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