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<b>let </b><font color="Maroon">Q</font> be   <a href="quantal1.html#NM5">Girard-Quantale</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">Q</font>;<br/>



<a NAME="E1:72"/>
(  <a href="quantal1.html#K4" target="_self">Top</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="quantal1.html#K3" target="_self">Bottom</a> <font color="Maroon">Q</font></span>)</span> <a href="quantal1.html#K1" target="_self">-r&gt;</a> <span class="p1">(<span class="default"><a href="quantal1.html#K3" target="_self">Bottom</a> <font color="Maroon">Q</font></span>)</span> &amp;  <a href="quantal1.html#K3" target="_self">Bottom</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> the <a href="quantal1.html#U1" target="_self">absurd</a> of <font color="Maroon">Q</font> &amp; the <a href="quantal1.html#U1" target="_self">absurd</a> of <font color="Maroon">Q</font> is <a href="quantal1.html#V17" target="_self">dualizing</a> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:72"/><b>then </b>
(  <a href="quantal1.html#K4" target="_self">Top</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Maroon">Q</font>) &amp; <font color="Maroon">H<sub>4</sub></font>(<font color="Maroon">Q</font>) <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  )
 
<b>by </b><i>, <a class="ref" href="monoid_0.html#D10">MONOID_0:def 10</a></i>;<br/>
<a NAME="E3:72"/><b>then </b>
( <font color="Maroon">H<sub>4</sub></font>(<font color="Maroon">Q</font>) <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><a href="quantal1.html#K4" target="_self">Top</a> <font color="Maroon">Q</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">H<sub>4</sub></font>(<font color="Maroon">Q</font>) <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="quantal1.html#K4" target="_self">Top</a> <font color="Maroon">Q</font></span>)</span>,<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 
<b>by </b><i><a class="ref" href="setwiseo.html#T23">SETWISEO:23</a></i>;<br/>
<b>hence </b><a NAME="E4:72"/>
( <font color="Maroon">a</font> <a href="monoid_0.html#NK3" target="_self">[*]</a> <span class="p1">(<span class="default"><a href="quantal1.html#K4" target="_self">Top</a> <font color="Maroon">Q</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><a href="quantal1.html#K4" target="_self">Top</a> <font color="Maroon">Q</font></span>)</span> <a href="monoid_0.html#NK3" target="_self">[*]</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="group_1.html#D1">GROUP_1:def 1</a></i>;<br/>


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