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<div><span class="kw">theorem </span><a NAME="T20"><span class="comment"><font color="firebrick">:: QUANTAL1:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Q</font> being   <a href="quantal1.html#NM1" title="QUANTAL1:NM.1">Quantale</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">Q</font>  st <font color="Olive" title="b2">a</font> is  <a href="quantal1.html#V17" title="QUANTAL1:attr.17">dualizing</a>  holds <br/>( <font color="Olive" title="b3">b</font> <a href="quantal1.html#K1" title="QUANTAL1:func.1">-r&gt;</a> <font color="Olive" title="b4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">b</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">c</font> <a href="quantal1.html#K2" title="QUANTAL1:func.2">-l&gt;</a> <font color="Olive" title="b2">a</font></span>)</span></span>)</span> <a href="quantal1.html#K1" title="QUANTAL1:func.1">-r&gt;</a> <font color="Olive" title="b2">a</font> &amp; <font color="Olive" title="b3">b</font> <a href="quantal1.html#K2" title="QUANTAL1:func.2">-l&gt;</a> <font color="Olive" title="b4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">c</font> <a href="quantal1.html#K1" title="QUANTAL1:func.1">-r&gt;</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="quantal1.html#K2" title="QUANTAL1:func.2">-l&gt;</a> <font color="Olive" title="b2">a</font> )</div></div>
