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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<b>reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font>, <font color="Maroon">y'</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/>
<a NAME="E2:47"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">x'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x'</font> &amp; <font color="Maroon">y'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y'</font> )
 
;<br/>
<b>assume </b><a NAME="E3:47"/>
 <a href="waybel_0.html#K5" target="_self">downarrow</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K5" target="_self">downarrow</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E4:47"/><b>then </b>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K5" target="_self">downarrow</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K5" target="_self">downarrow</a> <font color="Maroon">y</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:47"/><b>then </b>
( <font color="Maroon">x'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y'</font> &amp; <font color="Maroon">x'</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">y'</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:47"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="orders_2.html#T25">ORDERS_2:25</a></i>;<br/>


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