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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">antisymmetric</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c2">a1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c3">a2</font>
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c3">a2</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c2">a1</font>
 ;<br/>

<a NAME="E3:18"/>
<font color="Maroon" title="c3">a2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">a1</font>
 
<b>by </b><i><a class="txt" href="orders_2.html#E2:18"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="orders_2.html#D10" target="_self" title="ORDERS_2:def.10">Def10</a></i>;<br/>
<b>hence </b><a NAME="E4:18"/>
contradiction
 <b>by </b><i><a class="txt" href="orders_2.html#E1:18"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="orders_2.html#E2:18"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="orders_2.html#T25" target="_self" title="ORDERS_2:th.25">Th25</a></i>;<br/>


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