--- /dev/null
+<table frame="topbot" rowsep="0" colsep="0" role="grammar">
+ <title>tactics</title>
+ <tgroup cols="3">
+ <tbody>
+ <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>
+ </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>
+ </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>
+ </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>
+ </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>
+ </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>
+ </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>
+ </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>
+ </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 role="bold">by</emphasis> [ <emphasis><link linkend="grammar.term">term</link></emphasis> | <emphasis role="bold">_</emphasis> [<emphasis role="bold">(</emphasis><emphasis><link linkend="grammar.autoparams">auto_params</link></emphasis><emphasis role="bold">)</emphasis>]] [<emphasis role="bold">done</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>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><emphasis role="bold">the thesis becomes</emphasis> <emphasis><link linkend="grammar.sterm">sterm</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>
+ </row>
+ </tbody>
+ </tgroup>
+</table>
--- /dev/null
+<table frame="topbot" rowsep="0" colsep="0" role="grammar">
+ <title>tactics</title>
+ <tgroup cols="3">
+ <tbody>
+ <row>
+ <entry id="grammar.tactic">&tactic;</entry>
+ <entry>::=</entry>
+ <entry><link linkend="tac_absurd"><emphasis role="bold">absurd</emphasis></link> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_apply"><emphasis role="bold">apply</emphasis></link> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_applyS"><emphasis role="bold">applyS</emphasis></link> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis> <emphasis><link linkend="grammar.autoparams">auto_params</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_assumption">
+ <emphasis role="bold">assumption</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_auto"><emphasis role="bold">auto</emphasis></link> <emphasis><link linkend="grammar.autoparams">auto_params</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_change"><emphasis role="bold">change</emphasis></link> <emphasis><link linkend="grammar.pattern">pattern</link></emphasis> <emphasis role="bold">with</emphasis> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_clear"><emphasis role="bold">clear</emphasis></link>
+ <emphasis><link linkend="grammar.id">id</link></emphasis> [<emphasis><link linkend="grammar.id">id</link></emphasis>…]
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_clearbody"><emphasis role="bold">clearbody</emphasis></link> <emphasis><link linkend="grammar.id">id</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_constructor"><emphasis role="bold">constructor</emphasis></link> <emphasis><link linkend="grammar.nat">nat</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_contradiction">
+ <emphasis role="bold">contradiction</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_cut"><emphasis role="bold">cut</emphasis></link> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis> [<emphasis role="bold">as</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis>]</entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_decompose"><emphasis role="bold">decompose</emphasis></link>
+ [<emphasis role="bold">(</emphasis>
+ <emphasis><link linkend="grammar.id">id</link></emphasis>…
+ <emphasis role="bold">)</emphasis>]
+ [<emphasis><link linkend="grammar.id">id</link></emphasis>]
+ [<emphasis role="bold">as</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis>…]
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_demodulate">
+ <emphasis role="bold">demodulate</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_destruct"><emphasis role="bold">destruct</emphasis></link> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_elim"><emphasis role="bold">elim</emphasis></link> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis> [<emphasis role="bold">using</emphasis> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis>] <emphasis><link linkend="grammar.intros-spec">intros-spec</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_elimType"><emphasis role="bold">elimType</emphasis></link> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis> [<emphasis role="bold">using</emphasis> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis>] <emphasis><link linkend="grammar.intros-spec">intros-spec</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_exact"><emphasis role="bold">exact</emphasis></link> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_exists">
+ <emphasis role="bold">exists</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_fail">
+ <emphasis role="bold">fail</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_fold"><emphasis role="bold">fold</emphasis></link> <emphasis><link linkend="grammar.reduction-kind">reduction-kind</link></emphasis> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis> <emphasis><link linkend="grammar.pattern">pattern</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_fourier">
+ <emphasis role="bold">fourier</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_fwd"><emphasis role="bold">fwd</emphasis></link> <emphasis><link linkend="grammar.id">id</link></emphasis> [<emphasis role="bold">as</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis> [<emphasis><link linkend="grammar.id">id</link></emphasis>]…]</entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_generalize"><emphasis role="bold">generalize</emphasis></link> <emphasis><link linkend="grammar.pattern">pattern</link></emphasis> [<emphasis role="bold">as</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis>]</entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_id">
+ <emphasis role="bold">id</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_intro"><emphasis role="bold">intro</emphasis></link> [<emphasis><link linkend="grammar.id">id</link></emphasis>]</entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_intros"><emphasis role="bold">intros</emphasis></link> <emphasis><link linkend="grammar.intros-spec">intros-spec</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_inversion"><emphasis role="bold">inversion</emphasis></link> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_lapply"><emphasis role="bold">lapply</emphasis></link>
+ [<emphasis role="bold">linear</emphasis>]
+ [<emphasis role="bold">depth=</emphasis><emphasis><link linkend="grammar.nat">nat</link></emphasis>]
+ <emphasis><link linkend="grammar.sterm">sterm</link></emphasis>
+ [<emphasis role="bold">to</emphasis>
+ <emphasis><link linkend="grammar.sterm">sterm</link></emphasis>
+ [<emphasis role="bold">,</emphasis><emphasis><link linkend="grammar.sterm">sterm</link></emphasis>…]
+ ]
+ [<emphasis role="bold">as</emphasis> <emphasis><link linkend="grammar.id">id</link></emphasis>]
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_left">
+ <emphasis role="bold">left</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_letin"><emphasis role="bold">letin</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><link linkend="tac_normalize"><emphasis role="bold">normalize</emphasis></link> <emphasis><link linkend="grammar.pattern">pattern</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_reduce"><emphasis role="bold">reduce</emphasis></link> <emphasis><link linkend="grammar.pattern">pattern</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_reflexivity">
+ <emphasis role="bold">reflexivity</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_replace"><emphasis role="bold">replace</emphasis></link> <emphasis><link linkend="grammar.pattern">pattern</link></emphasis> <emphasis role="bold">with</emphasis> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_rewrite"><emphasis role="bold">rewrite</emphasis></link> [<emphasis role="bold"><</emphasis>|<emphasis role="bold">></emphasis>] <emphasis><link linkend="grammar.sterm">sterm</link></emphasis> <emphasis><link linkend="grammar.pattern">pattern</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_right">
+ <emphasis role="bold">right</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_ring">
+ <emphasis role="bold">ring</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_simplify"><emphasis role="bold">simplify</emphasis></link> <emphasis><link linkend="grammar.pattern">pattern</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_split">
+ <emphasis role="bold">split</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_subst">
+ <emphasis role="bold">subst</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry>
+ <link linkend="tac_symmetry">
+ <emphasis role="bold">symmetry</emphasis>
+ </link>
+ </entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_transitivity"><emphasis role="bold">transitivity</emphasis></link> <emphasis><link linkend="grammar.sterm">sterm</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_unfold"><emphasis role="bold">unfold</emphasis></link> [<emphasis><link linkend="grammar.sterm">sterm</link></emphasis>] <emphasis><link linkend="grammar.pattern">pattern</link></emphasis></entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><link linkend="tac_whd"><emphasis role="bold">whd</emphasis></link> <emphasis><link linkend="grammar.pattern">pattern</link></emphasis></entry>
+ </row>
+ </tbody>
+ </tgroup>
+</table>