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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th19</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: ALTCAT_1:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">o</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="altcat_1.html#K9" title="ALTCAT_1:func.9">DiscrCat</a> <font color="Olive" title="b1">A</font></span>)</span> holds   the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <span class="p1">(<span class="default"><a href="altcat_1.html#K9" title="ALTCAT_1:func.9">DiscrCat</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> (<font color="Olive" title="b2">o</font>,<font color="Olive" title="b2">o</font>,<font color="Olive" title="b2">o</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<span class="p1">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <font color="Olive" title="b2">o</font></span>)</span>,<span class="p1">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <font color="Olive" title="b2">o</font></span>)</span>) <a href="funcop_1.html#K18" title="FUNCOP_1:func.18">:-&gt;</a> <span class="p1">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <font color="Olive" title="b2">o</font></span>)</span></div></div>
