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<b>let </b><font color="Maroon">s</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">t</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:16_1_2"/><i><font color="Green">E53</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s</font>
 <b>and </b><br/><a NAME="E2:16_1_2"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E3:16_1_2"/><i><font color="Green">E58</font></i>: 
for <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t</font>
 <b>and </b><br/><a NAME="E4:16_1_2"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<b>consider </b><font color="Maroon">A</font> being  non <a href="xboole_0.html#V1">empty</a> <a href="orders_2.html#NM2">Chain</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E6:16_1_2"/><i><font color="Green">E60</font></i>: 
( ( for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s</font> ) &amp; <font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <b>and </b><br/><a NAME="E7:16_1_2"/><i><font color="Green">E61</font></i>: 
( ( for <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t</font> ) &amp; <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <b>by </b><i>, , , </i>;<br/>
<a NAME="E8:16_1_2"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">t</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:16_1_2"/>
<font color="Maroon">s</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E10:16_1_2"/>
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i>, <a class="ref" href="orders_2.html#T25">ORDERS_2:25</a></i>;<br/>


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