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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ;<br/><b>let </b><font color="Maroon" title="c2">e</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c3">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<b>set </b><font color="Maroon" title="c4">N</font> =  <a href="waybel11.html#K4" title="WAYBEL11:func.4">Net-Str</a> <font color="Maroon" title="c2">e</font>;<br/>
<a NAME="E1:61"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K4" title="WAYBEL11:func.4">Net-Str</a> <font color="Maroon" title="c2">e</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="waybel11.html#D11" target="_self" title="WAYBEL11:def.11">Def11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">d</font> = <font color="Maroon" title="c2">e</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K4" title="WAYBEL11:func.4">Net-Str</a> <font color="Maroon" title="c2">e</font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:61_1"/>
 <a href="waybel11.html#K4" title="WAYBEL11:func.4">Net-Str</a> <font color="Maroon" title="c2">e</font> <a href="waybel_0.html#R1" title="WAYBEL_0:pred.1">is_eventually_in</a> <font color="Maroon" title="c3">X</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c6">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K4" title="WAYBEL11:func.4">Net-Str</a> <font color="Maroon" title="c2">e</font></span>)</span><b> such that </b><br/><a NAME="E3:61_1"/><i><font color="Green" title="E33">A1</font></i>: 
for <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K4" title="WAYBEL11:func.4">Net-Str</a> <font color="Maroon" title="c2">e</font></span>)</span>  st <font color="Maroon" title="c6">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b1">y</font> holds <br/><span class="p1">(<span class="default"><a href="waybel11.html#K4" title="WAYBEL11:func.4">Net-Str</a> <font color="Maroon" title="c2">e</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="ref" href="waybel_0.html#D11" title="WAYBEL_0:def.11">WAYBEL_0:def 11</a></i>;<br/><a NAME="E4:61_1"/>
<span class="p1">(<span class="default"><a href="waybel11.html#K4" title="WAYBEL11:func.4">Net-Str</a> <font color="Maroon" title="c2">e</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="waybel11.html#E3:61_1"><i><font color="Green" title="E33">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E5:61_1"/>
<font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="ref" href="waybel11.html#T26" target="_self" title="WAYBEL11:th.26">Th26</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E4:61"/><i><font color="Green" title="E33">A2</font></i>: 
<font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 ;<br/>

<b>take </b>
<font color="Maroon" title="c5">d</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D11" title="WAYBEL_0:def.11">WAYBEL_0:def 11</a><br/>

<b>let </b><font color="Maroon" title="c6">j</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K4" title="WAYBEL11:func.4">Net-Str</a> <font color="Maroon" title="c2">e</font></span>)</span>;<br/>

<b>assume </b><a NAME="E5:61"/>
<font color="Maroon" title="c5">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">j</font>
 ;<br/>

<b>thus </b><a NAME="E6:61"/>
<span class="p1">(<span class="default"><a href="waybel11.html#K4" title="WAYBEL11:func.4">Net-Str</a> <font color="Maroon" title="c2">e</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c6">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="waybel11.html#E4:61"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="waybel11.html#T26" target="_self" title="WAYBEL11:th.26">Th26</a></i>;<br/>


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