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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th63</font></span>: <a NAME="T63"><span class="comment"><font color="firebrick">:: ORDERS_1:63</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a><br/>  for <font color="Olive" title="b2">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">R</font> <a href="orders_1.html#R2" title="ORDERS_1:pred.2">partially_orders</a> <font color="Olive" title="b2">X</font> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">X</font> &amp; <font color="Olive" title="b2">X</font> <a href="orders_1.html#R4" title="ORDERS_1:pred.4">has_upper_Zorn_property_wrt</a> <font color="Olive" title="b1">R</font> holds <br/> ex <font color="Olive" title="b3">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <font color="Olive" title="b3">x</font> <a href="orders_1.html#R6" title="ORDERS_1:pred.6">is_maximal_in</a> <font color="Olive" title="b1">R</font></div></div>
