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<div><span class="kw">theorem </span><a NAME="T12"><span class="comment"><font color="firebrick">:: YELLOW10:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span> holds <br/> (  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span> iff (  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">x</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b4">y</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Olive" title="b1">S</font> &amp;  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">x</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b4">y</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Olive" title="b2">T</font> ) )</div></div>
