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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: YELLOW21:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="yellow_0.html#V2" title="YELLOW_0:attr.2">upper-bounded</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>  st  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Olive" title="b1">P</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>  holds <br/> for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">P</font>  st <font color="Olive" title="b3">y</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Olive" title="b2">x</font> holds <br/> ex <font color="Olive" title="b4">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">P</font> st <br/>( <font color="Olive" title="b4">z</font> is  <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a>  &amp; <font color="Olive" title="b3">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b4">z</font> &amp; <font color="Olive" title="b4">z</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">x</font> )</div></div>
