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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: RINGCAT1:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">UN</font> being   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a><br/>  for <font color="Olive" title="b2">a</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="ringcat1.html#K17" title="RINGCAT1:func.17">RingCat</a> <font color="Olive" title="b1">UN</font></span>)</span><br/>  for <font color="Olive" title="b3">aa</font> being    <a href="ringcat1.html#M2" title="RINGCAT1:mode.2">Element</a> of  <a href="ringcat1.html#K9" title="RINGCAT1:func.9">RingObjects</a> <font color="Olive" title="b1">UN</font>  st <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">aa</font> holds <br/> <a href="cat_1.html#K4" title="CAT_1:func.4">id</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#K13" title="RINGCAT1:func.13">ID</a> <font color="Olive" title="b3">aa</font></div></div>
