<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: YELLOW21:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">W</font> being   <a href="setfam_1.html#NV3" title="SETFAM_1:NV.3">with_non-empty_element</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">W</font> <a href="yellow21.html#K6" title="YELLOW21:func.6">-UPS_category</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="yellow21.html#K2" title="YELLOW21:func.2">POSETS</a> <font color="Olive" title="b1">W</font></div></div>
