matita/help/C/declarative_tactics_quickref.xml

   1 <table frame="topbot" rowsep="0" colsep="0" role="grammar">
   2   <title>tactics</title>
   3   <tgroup cols="3">
   4     <tbody>
   5       <row>
   6         <entry id="grammar.declarative_tactic">&tactic;</entry>
   7         <entry>::=</entry>
   8         <entry><emphasis role="bold">we need to prove</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> </entry>
   9       </row>
  10       <row>
  11         <entry/>
  12         <entry>|</entry>
  13         <entry><emphasis role="bold">we proceed by induction on</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> <emphasis role="bold"> to prove </emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> </entry>
  14       </row>
  15       <row>
  16         <entry/>
  17         <entry>|</entry>
  18         <entry><link linkend="tac_assume"><emphasis role="bold">assume</emphasis></link> <emphasis><link linkend="grammar.id">id</link></emphasis> <emphasis role="bold"> : </emphasis> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis></entry>
  19       </row>
  20       <row>
  21         <entry/>
  22         <entry>|</entry>
  23         <entry><emphasis role="bold">by</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> <emphasis role="bold"> done </emphasis></entry>
  24       </row>
  25       <row>
  26         <entry/>
  27         <entry>|</entry>
  28         <entry><emphasis role="bold">by induction hypothesis we know</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> <emphasis role="bold"> (</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis> <emphasis role="bold">)</emphasis></entry>
  29       </row>
  30       <row>
  31         <entry/>
  32         <entry>|</entry>
  33         <entry><emphasis role="bold">by</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> <emphasis role="bold">we proved</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis>
  34                    <emphasis role="bold">(</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis> <emphasis role="bold">)</emphasis></entry>
  35       </row>
  36       <row>
  37         <entry/>
  38         <entry>|</entry>
  39         <entry><link linkend="tac_case"><emphasis role="bold">case</emphasis></link> <emphasis><link linkend="grammar.id">id</link></emphasis> <emphasis role="bold">(</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis> <emphasis role="bold">:</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> <emphasis role="bold">)</emphasis></entry>
  40       </row>
  41       <row>
  42         <entry/>
  43         <entry>|</entry>
  44         <entry><emphasis role="bold">by</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> <emphasis role="bold">let</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis>
  45                     <emphasis role="bold">:</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> <emphasis role="bold">such that</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis>
  46                      <emphasis role="bold">(</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis> <emphasis role="bold">)</emphasis></entry>
  47       </row>
  48       <row>
  49         <entry/>
  50         <entry>|</entry>
  51         <entry>[<emphasis role="bold">obtain</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis> | <emphasis role="bold">conclude</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis>] <emphasis role="bold">=</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> [<emphasis><link linkend="grammar.autoparams">auto_params</link></emphasis> | <emphasis role="bold">exact</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> | <emphasis role="bold">using</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> | <emphasis role="bold">proof</emphasis>] [<emphasis role="bold">done</emphasis>]</entry>
  52       </row>
  53       <row>
  54         <entry/>
  55         <entry>|</entry>
  56         <entry><link linkend="tac_suppose"><emphasis role="bold">suppose</emphasis></link> <emphasis><link linkend="grammar.term">term</link></emphasis> <emphasis role="bold"> (</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis>
  57              <emphasis role="bold">) </emphasis> [ that is equivalent to  <emphasis><link linkend="grammar.term">term</link></emphasis> ]</entry>
  58       </row>
  59       <row>
  60         <entry/>
  61         <entry>|</entry>
  62         <entry><emphasis role="bold">the thesis becomes</emphasis> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis> </entry>
  63       </row>
  64       <row>
  65         <entry/>
  66         <entry>|</entry>
  67         <entry><emphasis role="bold">we proceed by cases on </emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> <emphasis role="bold">to prove</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> </entry>
  68       </row>
  69     </tbody>
  70   </tgroup>
  71 </table>