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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="orders_2.html#V4" target="_self">antisymmetric</a>  <a href="orders_2.html#L1" target="_self">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R2" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:18"/>
<font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="orders_2.html#E2:18"><i><font color="Green">E14</font></i></a>, <a class="ref" href="orders_2.html#D10" target="_self">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">E13</font></i></a>, <a class="txt" href="orders_2.html#E2:18"><i><font color="Green">E14</font></i></a>, <a class="ref" href="orders_2.html#T25" target="_self">Th25</a></i>;<br/>


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