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

<b>let </b><font color="Maroon">L</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">N</font> be   <a href="waybel_0.html#NM2">net</a> of <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>;<br/>





<b>assume </b><a NAME="E1:25"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">N</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7">NetUniv</a> <font color="Maroon">L</font>
 ;<br/>

<b>hence </b><a NAME="E2:25"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">N</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="waybel28.html#K3" target="_self">lim_inf-Convergence</a> <font color="Maroon">L</font> implies for <font color="Olive">M</font> being   <a href="yellow_6.html#M2">subnet</a> of <font color="Maroon">N</font>  st <font color="Olive">M</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7">NetUniv</a> <font color="Maroon">L</font> holds <br/><font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="waybel11.html#K1">lim_inf</a> <font color="Olive">M</font> )
 <b>by </b><i/>;<br/>

<b>assume </b><a NAME="E3:25"/>
for <font color="Olive">M</font> being   <a href="yellow_6.html#M2">subnet</a> of <font color="Maroon">N</font>  st <font color="Olive">M</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7">NetUniv</a> <font color="Maroon">L</font> holds <br/><font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="waybel11.html#K1">lim_inf</a> <font color="Olive">M</font>
 ;<br/>

<a NAME="E4:25"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="waybel11.html#K1">lim_inf</a> <font color="Maroon">N</font> &amp; ( for <font color="Olive">M</font> being   <a href="yellow_6.html#M2">subnet</a> of <font color="Maroon">N</font>  st <font color="Olive">M</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7">NetUniv</a> <font color="Maroon">L</font> holds <br/><font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a>  <a href="waybel_9.html#K2">inf</a> <font color="Olive">M</font> ) )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:25"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="waybel11.html#K1">lim_inf</a> <font color="Maroon">N</font> &amp; ( for <font color="Olive">p</font> being <a href="waybel28.html#V1" target="_self">greater_or_equal_to_id</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">N</font>,<font color="Maroon">N</font> holds  <font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a>  <a href="waybel_9.html#K2">inf</a> <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel28.html#K2" target="_self">*</a> <font color="Olive">p</font></span>)</span> ) )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:25"/><b>then </b>
for <font color="Olive">M</font> being   <a href="yellow_6.html#M2">subnet</a> of <font color="Maroon">N</font> holds  <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="waybel11.html#K1">lim_inf</a> <font color="Olive">M</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:25"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">N</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="waybel28.html#K3" target="_self">lim_inf-Convergence</a> <font color="Maroon">L</font>
 <b>by </b><i>, </i>;<br/>


</div>
