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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: ORDERS_2:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</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="b2">a1</font>, <font color="Olive" title="b3">a2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">A</font> holds <br/> (  ex <font color="Olive" title="b4">C</font> being   <a href="orders_2.html#NM2" title="ORDERS_2:NM.2">Chain</a> of <font color="Olive" title="b1">A</font> st <br/>( <font color="Olive" title="b2">a1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">C</font> &amp; <font color="Olive" title="b3">a2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">C</font> ) iff ( <font color="Olive" title="b2">a1</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Olive" title="b3">a2</font> iff  not <font color="Olive" title="b3">a2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b2">a1</font> ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="orders_2.html#T6" target="_self" onmouseover="rs('orders_2/T6')" onmouseout="rh()">Th6</a>, <a class="ref" href="orders_2.html#T11" target="_self" onmouseover="rs('orders_2/T11')" onmouseout="rh()">Th11</a></span>;<br/></div></div>
