<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">e</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>set </b><font color="Maroon">N</font> =  <a href="waybel11.html#K4" target="_self">Net-Str</a> <font color="Maroon">e</font>;<br/>
<a NAME="E1:62"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K4" target="_self">Net-Str</a> <font color="Maroon">e</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">e</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">e</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K4" target="_self">Net-Str</a> <font color="Maroon">e</font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:62_1"/>
 <a href="waybel11.html#K4" target="_self">Net-Str</a> <font color="Maroon">e</font> <a href="waybel_0.html#R1">is_eventually_in</a> <font color="Maroon">X</font>
 ;<br/><b>then consider </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K4" target="_self">Net-Str</a> <font color="Maroon">e</font></span>)</span><b> such that </b><br/><a NAME="E3:62_1"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K4" target="_self">Net-Str</a> <font color="Maroon">e</font></span>)</span>  st <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">y</font> holds <br/><span class="p1">(<span class="default"><a href="waybel11.html#K4" target="_self">Net-Str</a> <font color="Maroon">e</font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="waybel_0.html#D11">WAYBEL_0:def 11</a></i>;<br/><a NAME="E4:62_1"/>
<span class="p1">(<span class="default"><a href="waybel11.html#K4" target="_self">Net-Str</a> <font color="Maroon">e</font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E5:62_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E4:62"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<b>take </b>
<font color="Maroon">d</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D11">WAYBEL_0:def 11</a><br/>

<b>let </b><font color="Maroon">j</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K4" target="_self">Net-Str</a> <font color="Maroon">e</font></span>)</span>;<br/>

<b>assume </b><a NAME="E5:62"/>
<font color="Maroon">d</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">j</font>
 ;<br/>

<b>thus </b><a NAME="E6:62"/>
<span class="p1">(<span class="default"><a href="waybel11.html#K4" target="_self">Net-Str</a> <font color="Maroon">e</font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i>, </i>;<br/>


</div>
