<row>
<entry id="grammar.declarative_tactic">&tactic;</entry>
<entry>::=</entry>
- <entry><emphasis role="bold">we need to prove</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> </entry>
+ <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>
</row>
<row>
<entry/>
<entry>|</entry>
- <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>
+ <entry><link linkend="tac_by induction hypothesis we know"><emphasis role="bold">by induction hypothesis we know</emphasis></link> <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>
</row>
<row>
<entry/>
<entry>|</entry>
- <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>
+ <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>
</row>
<row>
<entry/>
<entry>|</entry>
- <entry><emphasis role="bold">by</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> <emphasis role="bold"> done </emphasis></entry>
+ <entry><emphasis><link linkend="grammar.justification">justification</link></emphasis> <link linkend="tac_done"><emphasis role="bold">done</emphasis></link></entry>
</row>
<row>
<entry/>
<entry>|</entry>
- <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>
+ <entry><emphasis><link linkend="grammar.justification">justification</link></emphasis> <emphasis role="bold">let</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis>
+ <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>
+ <emphasis role="bold">(</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis> <emphasis role="bold">)</emphasis></entry>
</row>
<row>
<entry/>
<entry>|</entry>
- <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>
- <emphasis role="bold">(</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis> <emphasis role="bold">)</emphasis></entry>
+ <entry>[<link linkend="tac_obtain"><emphasis role="bold">obtain</emphasis></link> <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">using</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> | <emphasis role="bold">using once</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> | <emphasis role="bold">proof</emphasis>] [<emphasis role="bold">done</emphasis>]</entry>
</row>
<row>
<entry/>
<entry>|</entry>
- <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>
+ <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>
+ <emphasis role="bold">) </emphasis> [ <emphasis role="bold">that is equivalent to</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> ]</entry>
</row>
<row>
<entry/>
<entry>|</entry>
- <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>
- <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>
- <emphasis role="bold">(</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis> <emphasis role="bold">)</emphasis></entry>
+ <entry><link linkend="tac_the thesis becomes"><emphasis role="bold">the thesis becomes</emphasis></link> <emphasis><link linkend="grammar.term">term</link></emphasis> </entry>
</row>
<row>
<entry/>
<entry>|</entry>
- <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>
+ <entry><link linkend="tac_we need to prove"><emphasis role="bold">we need to prove</emphasis></link> <emphasis><link linkend="grammar.term">term</link></emphasis>
+ [<emphasis role="bold">(</emphasis><emphasis><link linkend="grammar.id">id</link></emphasis>
+ <emphasis role="bold">)</emphasis>]
+ [ <emphasis role="bold">or equivalently</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis>]</entry>
</row>
<row>
<entry/>
<entry>|</entry>
- <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>
- <emphasis role="bold">) </emphasis> [ that is equivalent to <emphasis><link linkend="grammar.term">term</link></emphasis> ]</entry>
+ <entry><link linkend="tac_we proceed by cases on"><emphasis role="bold">we proceed by cases on</emphasis></link> <emphasis><link linkend="grammar.term">term</link></emphasis> <emphasis role="bold">to prove</emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> </entry>
</row>
<row>
<entry/>
<entry>|</entry>
- <entry><emphasis role="bold">the thesis becomes</emphasis> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis> </entry>
+ <entry><link linkend="tac_we proceed by induction on"><emphasis role="bold">we proceed by induction on</emphasis></link> <emphasis><link linkend="grammar.term">term</link></emphasis> <emphasis role="bold"> to prove </emphasis> <emphasis><link linkend="grammar.term">term</link></emphasis> </entry>
</row>
<row>
<entry/>
<entry>|</entry>
- <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>
+ <entry><emphasis><link linkend="grammar.justification">justification</link></emphasis> <link linkend="tac_we proved"><emphasis role="bold">we proved</emphasis></link> <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>
</row>
</tbody>
</tgroup>