| 13305 |      1 | %
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|  |      2 | \begin{isabellebody}%
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|  |      3 | \def\isabellecontext{Plus}%
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| 17056 |      4 | %
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|  |      5 | \isadelimtheory
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|  |      6 | %
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|  |      7 | \endisadelimtheory
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|  |      8 | %
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|  |      9 | \isatagtheory
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|  |     10 | %
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|  |     11 | \endisatagtheory
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|  |     12 | {\isafoldtheory}%
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|  |     13 | %
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|  |     14 | \isadelimtheory
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|  |     15 | %
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|  |     16 | \endisadelimtheory
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| 13305 |     17 | %
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|  |     18 | \begin{isamarkuptext}%
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|  |     19 | \noindent Define the following addition function%
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|  |     20 | \end{isamarkuptext}%
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| 17175 |     21 | \isamarkuptrue%
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|  |     22 | \isacommand{primrec}\isamarkupfalse%
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| 27015 |     23 | \ add\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
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|  |     24 | {\isachardoublequoteopen}add\ m\ {\isadigit{0}}\ {\isacharequal}\ m{\isachardoublequoteclose}\ {\isacharbar}\isanewline
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| 19249 |     25 | {\isachardoublequoteopen}add\ m\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ add\ {\isacharparenleft}Suc\ m{\isacharparenright}\ n{\isachardoublequoteclose}%
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| 13305 |     26 | \begin{isamarkuptext}%
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|  |     27 | \noindent and prove%
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|  |     28 | \end{isamarkuptext}%
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| 17175 |     29 | \isamarkuptrue%
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| 17056 |     30 | %
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|  |     31 | \isadelimproof
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|  |     32 | %
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|  |     33 | \endisadelimproof
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|  |     34 | %
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|  |     35 | \isatagproof
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|  |     36 | %
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|  |     37 | \endisatagproof
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|  |     38 | {\isafoldproof}%
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|  |     39 | %
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|  |     40 | \isadelimproof
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|  |     41 | %
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|  |     42 | \endisadelimproof
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| 17175 |     43 | \isacommand{lemma}\isamarkupfalse%
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| 19249 |     44 | \ {\isachardoublequoteopen}add\ m\ n\ {\isacharequal}\ m{\isacharplus}n{\isachardoublequoteclose}%
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| 17056 |     45 | \isadelimproof
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|  |     46 | %
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|  |     47 | \endisadelimproof
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|  |     48 | %
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|  |     49 | \isatagproof
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|  |     50 | %
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|  |     51 | \endisatagproof
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|  |     52 | {\isafoldproof}%
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|  |     53 | %
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|  |     54 | \isadelimproof
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|  |     55 | %
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|  |     56 | \endisadelimproof
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|  |     57 | %
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|  |     58 | \isadelimtheory
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|  |     59 | %
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|  |     60 | \endisadelimtheory
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|  |     61 | %
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|  |     62 | \isatagtheory
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|  |     63 | %
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|  |     64 | \endisatagtheory
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|  |     65 | {\isafoldtheory}%
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|  |     66 | %
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|  |     67 | \isadelimtheory
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|  |     68 | %
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|  |     69 | \endisadelimtheory
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| 13305 |     70 | \end{isabellebody}%
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|  |     71 | %%% Local Variables:
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|  |     72 | %%% mode: latex
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|  |     73 | %%% TeX-master: "root"
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|  |     74 | %%% End:
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