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<b>let </b><font color="Maroon" title="c1">Q</font> be   <a href="quantal1.html#NM5" title="QUANTAL1:NM.5">Girard-Quantale</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> holds <br/> ( <font color="Olive" title="b1">a</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p1">(<span class="default"><a href="quantal1.html#K4" title="QUANTAL1:func.4">Top</a> <font color="Maroon" title="c1">Q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <span class="p1">(<span class="default"><a href="quantal1.html#K4" title="QUANTAL1:func.4">Top</a> <font color="Maroon" title="c1">Q</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> )</span><br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p1">(<span class="default"><a href="quantal1.html#K4" title="QUANTAL1:func.4">Top</a> <font color="Maroon" title="c1">Q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <span class="p1">(<span class="default"><a href="quantal1.html#K4" title="QUANTAL1:func.4">Top</a> <font color="Maroon" title="c1">Q</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> )</span><br/>



<a NAME="E1:72"/>
(  <a href="quantal1.html#K4" title="QUANTAL1:func.4">Top</a> <font color="Maroon" title="c1">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="quantal1.html#K3" title="QUANTAL1:func.3">Bottom</a> <font color="Maroon" title="c1">Q</font></span>)</span> <a href="quantal1.html#K1" title="QUANTAL1:func.1">-r&gt;</a> <span class="p1">(<span class="default"><a href="quantal1.html#K3" title="QUANTAL1:func.3">Bottom</a> <font color="Maroon" title="c1">Q</font></span>)</span> &amp;  <a href="quantal1.html#K3" title="QUANTAL1:func.3">Bottom</a> <font color="Maroon" title="c1">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="quantal1.html#U1" title="QUANTAL1:sel.1">absurd</a> of <font color="Maroon" title="c1">Q</font> &amp; the <a href="quantal1.html#U1" title="QUANTAL1:sel.1">absurd</a> of <font color="Maroon" title="c1">Q</font> is <a href="quantal1.html#V17" title="QUANTAL1:attr.17">dualizing</a> )
 
<b>by </b><i><a class="ref" href="quantal1.html#D20" target="_self" title="QUANTAL1:def.20">Def20</a></i>;<br/>
<a NAME="E2:72"/><b>then </b>
(  <a href="quantal1.html#K4" title="QUANTAL1:func.4">Top</a> <font color="Maroon" title="c1">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Maroon" title="c1">Q</font>) &amp; <font color="Maroon">H<sub>4</sub></font>(<font color="Maroon" title="c1">Q</font>) is <a href="setwiseo.html#V1" title="SETWISEO:attr.1">having_a_unity</a> )
 
<b>by </b><i><a class="ref" href="quantal1.html#T19" target="_self" title="QUANTAL1:th.19">Th19</a>, <a class="ref" href="monoid_0.html#D10" title="MONOID_0:def.10">MONOID_0:def 10</a></i>;<br/>
<b>hence </b><a NAME="E3:72"/>
( <font color="Maroon" title="c2">a</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p1">(<span class="default"><a href="quantal1.html#K4" title="QUANTAL1:func.4">Top</a> <font color="Maroon" title="c1">Q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <span class="p1">(<span class="default"><a href="quantal1.html#K4" title="QUANTAL1:func.4">Top</a> <font color="Maroon" title="c1">Q</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> )
 <b>by </b><i><a class="ref" href="setwiseo.html#T23" title="SETWISEO:th.23">SETWISEO:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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