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<b>let </b><font color="Maroon">R</font> be  <a href="waybel_0.html#V25">/\-complete</a> <a href="waybel_0.html#NM6">Semilattice</a>;<br/><b>let </b><font color="Maroon">N</font> be   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">V</font> be  <a href="waybel_0.html#V12">lower</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>;<br/>





<b>consider </b><font color="Maroon">f</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">N</font>,<font color="Maroon">R</font><b> such that </b><br/><a NAME="E2:47"/><i><font color="Green">E32</font></i>: 
(  <a href="waybel32.html#K2" target="_self">inf_net</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <font color="Maroon">N</font> <a href="waybel32.html#K1" target="_self">*'</a> <font color="Maroon">f</font> &amp; ( for <font color="Olive">i</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> holds  <font color="Maroon">f</font> <a href="yellow_6.html#K3">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K2">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> : <font color="Olive">k</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">i</font> </span>}</span> ,<font color="Maroon">R</font> ) )
 <b>by </b><i/>;<br/>
<a NAME="E3:47"/><i><font color="Green">E36</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" target="_self">inf_net</a> <font color="Maroon">N</font></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" target="_self">inf_net</a> <font color="Maroon">N</font></span>)</span> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> #)
 
<b>by </b><i>, </i>;<br/>
<b>assume </b><a NAME="E4:47"/>
<font color="Maroon">N</font> <a href="waybel_0.html#R1">is_eventually_in</a> <font color="Maroon">V</font>
 ;<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="E6:47"/><i><font color="Green">E37</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="Maroon">i</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">j</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">V</font>
 <b>by </b><i><a class="ref" href="waybel_0.html#D11">WAYBEL_0:def 11</a></i>;<br/>
<b>reconsider </b><font color="Maroon">i'</font> = <font color="Maroon">i</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" target="_self">inf_net</a> <font color="Maroon">N</font></span>)</span> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">i'</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="waybel32.html#K2" target="_self">inf_net</a> <font color="Maroon">N</font></span>)</span>;<br/>

<b>assume </b><a NAME="E8:47"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">i'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">j</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">j0</font> = <font color="Maroon">j</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> <b>by </b><i/>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>] <b>means </b><font color="Maroon">a<sub>1</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">j0</font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> = <font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">E</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">k</font>) where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>] </span>}</span> ;<br/>
<b>consider </b><font color="Maroon">j1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E11:47"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">j1</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">j0</font> &amp; <font color="Maroon">j1</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">j0</font> )
 <b>by </b><i><a class="ref" href="yellow_6.html#D5">YELLOW_6:def 5</a></i>;<br/>
<a NAME="E12:47"/>
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">k</font>) where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>] </span>}</span>  is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>
 
<b>from </b><i><a class="ref" href="domain_1.html#S8">DOMAIN_1:sch 8</a>();<br/></i>
<b>then reconsider </b><font color="Maroon">E</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">k</font>) where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>] </span>}</span>  as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font> ;<br/>
<a NAME="E14:47"/>
( <font color="Maroon">i</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">j0</font> &amp; <font color="Maroon">j0</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">j1</font> )
 
<b>by </b><i>, , <a class="ref" href="waybel32.html#D1" target="_self">Def1</a>, <a class="ref" href="yellow_0.html#T1">YELLOW_0:1</a></i>;<br/>
<a NAME="E15:47"/><b>then </b>
<font color="Maroon">i</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">j1</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D2">YELLOW_0:def 2</a></i>;<br/>
<a NAME="E16:47"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">j1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 
<b>by </b><i/>;<br/>
<a NAME="E17:47"/>
<font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">j1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font>
 
<b>by </b><i><a class="ref" href="waybel32.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E18:47"/><b>then </b><i><font color="Green">E48</font></i>: 
 <a href="yellow_0.html#K2">"/\"</a> <font color="Maroon">E</font>,<font color="Maroon">R</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">j1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E19:47"/>
the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" target="_self">inf_net</a> <font color="Maroon">N</font></span>)</span> <a href="funct_2.html#R1">=</a> <font color="Maroon">f</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E20:47"/><b>then </b>
<span class="p1">(<span class="default"><a href="waybel32.html#K2" target="_self">inf_net</a> <font color="Maroon">N</font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K2">"/\"</a> <font color="Maroon">E</font>,<font color="Maroon">R</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E21:47"/>
<span class="p1">(<span class="default"><a href="waybel32.html#K2" target="_self">inf_net</a> <font color="Maroon">N</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">V</font>
 <b>by </b><i>, , <a class="ref" href="waybel_0.html#D19">WAYBEL_0:def 19</a></i>;<br/>


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