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<div><span class="kw">theorem </span><a NAME="T11"><span class="comment"><font color="firebrick">:: POSET_2:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</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">x</font>, <font color="Olive" title="b3">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Olive" title="b1">X</font> holds <br/> ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="poset_2.html#K3" title="POSET_2:func.3">FlatRelat</a> <font color="Olive" title="b1">X</font> iff ( <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X</font> or <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">y</font> ) ) <span class="kw">by</span> <span class="lab"><a class="txt" href="poset_2.html#E18"><span class="lab"><font color="Green" title="E16">LemFlatten01</font></span></a>, <a class="txt" href="poset_2.html#E19"><span class="lab"><font color="Green" title="E17">LemFlatten02</font></span></a></span>;<br/></div></div>
