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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#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">N</font> be   <a href="waybel_0.html#NM1">prenet</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:25"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">N</font> is <a href="waybel_0.html#V10">eventually-directed</a>
 ;<br/>

<b>set </b><font color="Maroon">f</font> =  <a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font>;<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>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D1">WAYBEL_0:def 1</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E2:25"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font></span>)</span>
 <b>and </b><br/><a NAME="E3:25"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font></span>)</span>
 ;<br/>

<b>consider </b><font color="Maroon">a</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:25"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon">b</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:25"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E8:25"/><i><font color="Green">E56</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">a</font>, <font color="Maroon">b</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> <b>by </b><i>, </i>;<br/>
<b>consider </b><font color="Maroon">ja</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E11:25"/><i><font color="Green">E58</font></i>: 
for <font color="Olive">k</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>  st <font color="Maroon">ja</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">k</font> holds <br/><font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Olive">k</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T11">WAYBEL_0:11</a></i>;<br/>
<b>consider </b><font color="Maroon">jb</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E13:25"/><i><font color="Green">E68</font></i>: 
for <font color="Olive">k</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>  st <font color="Maroon">jb</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">k</font> holds <br/><font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">b</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Olive">k</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T11">WAYBEL_0:11</a></i>;<br/>
<a NAME="E14:25"/><i><font color="Green">E71</font></i>: 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T12">PRE_TOPC:12</a></i>;<br/>
<a NAME="E15:25"/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font> is <a href="waybel_0.html#V1">directed</a>
 
<b>by </b><i><a class="ref" href="waybel_0.html#D6">WAYBEL_0:def 6</a></i>;<br/>
<b>then consider </b><font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E17:25"/><i><font color="Green">E72</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font> &amp; <font color="Maroon">ja</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">jb</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font> )
 <b>by </b><i>, <a class="ref" href="waybel_0.html#D1">WAYBEL_0:def 1</a></i>;<br/>
<b>take </b><font color="Maroon">z</font> = <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>;<br/>

<b>thus </b><a NAME="E18:25"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>

<a NAME="E19:25"/>
( <font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> &amp; <font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Maroon">N</font>,<font color="Maroon">L</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font> )
 
;<br/>
<b>hence </b><a NAME="E20:25"/>
( <font color="Maroon">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">z</font> )
 <b>by </b><i>, , , , </i>;<br/>


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