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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th41</font></span>: <a NAME="T41"><span class="comment"><font color="firebrick">:: WAYBEL12:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/>  for <font color="Olive" title="b2">A</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Olive" title="b1">T</font></span>)</span><br/>  for <font color="Olive" title="b3">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font>  st <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">B</font> &amp; <font color="Olive" title="b2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Olive" title="b1">T</font></span>)</span> holds <br/>( <font color="Olive" title="b2">A</font> is  <a href="waybel_6.html#NV3" title="WAYBEL_6:NV.3">irreducible</a>  iff <font color="Olive" title="b3">B</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="yellow_8.html#V3" title="YELLOW_8:attr.3">irreducible</a>  )</div></div>
