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<b>let </b><font color="Maroon">T</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#NM2">net</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>given </b><font color="Maroon">i'</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font><b> such that </b><a NAME="E1:52"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">j</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>  st <font color="Olive">j</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">i'</font> holds <br/><font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Olive">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D11">WAYBEL_0:def 11</a><br/>

<a NAME="E2:52"/>
(  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font> is <a href="waybel_0.html#V1">directed</a> &amp;  <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>, <a class="ref" href="waybel_0.html#D6">WAYBEL_0:def 6</a></i>;<br/>
<b>then consider </b><font color="Maroon">i</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E4:52"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font> &amp; <font color="Maroon">i'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">i</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">i</font>
;<br/>

<b>thus </b><a NAME="E5:52"/>
<font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i>, </i>;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E6:52"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K6">|</a> <font color="Maroon">i</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">j</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E8:52"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K6">|</a> <font color="Maroon">i</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K6">|</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E9:52"/><i><font color="Green">E38</font></i>: 
 <a href="relset_1.html#K4">dom</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K6">|</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K6">|</a> <font color="Maroon">i</font></span>)</span>
 
<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">j</font> = <font color="Maroon">j</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K6">|</a> <font color="Maroon">i</font></span>)</span> <b>by </b><i/>;<br/>
<a NAME="E11:52"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K6">|</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">y</font> where <font color="Olive">y</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> : <font color="Maroon">i</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">y</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="waybel_9.html#T12">WAYBEL_9:12</a></i>;<br/>
<b>then consider </b><font color="Maroon">k</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E13:52"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">i</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">k</font> )
 <b>by </b><i>, </i>;<br/>
<a NAME="E14:52"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">i'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">k</font>
 
<b>by </b><i>, <a class="ref" href="waybel21.html#T2" target="_self">Th2</a>, <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/>
<font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K6">|</a> <font color="Maroon">i</font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">j</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="waybel21.html#T2" target="_self">Th2</a>, <a class="ref" href="waybel_9.html#T16">WAYBEL_9:16</a></i>
;<br/>
<b>hence </b><a NAME="E16:52"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i>, </i>;<br/>


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