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

<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>;<br/><b>let </b><font color="Maroon" title="c2">N</font> be  <a href="yellow_6.html#V1" title="YELLOW_6:attr.1">constant</a> <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_6.html#D23" title="YELLOW_6:def.23">YELLOW_6:def 23</a><br/>



<b>assume </b><a NAME="E1:26"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c2">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c1">L</font>
 ;<br/>

<a NAME="E2:26"/>
for <font color="Olive" title="b1">M</font> being   <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Maroon" title="c2">N</font> holds   <a href="yellow_6.html#K5" title="YELLOW_6:func.5">the_value_of</a> <font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel11.html#K1" title="WAYBEL11:func.1">lim_inf</a> <font color="Olive" title="b1">M</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">M</font> be    <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Maroon" title="c2">N</font>;<br/>

<a NAME="E1:26_1"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c3">M</font> is <a href="yellow_6.html#V1" title="YELLOW_6:attr.1">constant</a>
 
<b>by </b><i><a class="ref" href="waybel28.html#T17" target="_self" title="WAYBEL28:th.17">Th17</a></i>;<br/>
<b>thus </b> <a href="yellow_6.html#K5" title="YELLOW_6:func.5">the_value_of</a> <font color="Maroon" title="c2">N</font> = 
 <a href="yellow_6.html#K5" title="YELLOW_6:func.5">the_value_of</a> <font color="Maroon" title="c3">M</font>
<b>by </b><i><a class="ref" href="waybel28.html#T17" target="_self" title="WAYBEL28:th.17">Th17</a></i>
<br/>.= 
 <a href="waybel11.html#K1" title="WAYBEL11:func.1">lim_inf</a> <font color="Maroon" title="c3">M</font>
<b>by </b><i><a class="txt" href="waybel28.html#E1:26_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="waybel11.html#T23" title="WAYBEL11:th.23">WAYBEL11:23</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:26"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">N</font>,<span class="p2">(<span class="default"><a href="yellow_6.html#K5" title="YELLOW_6:func.5">the_value_of</a> <font color="Maroon" title="c2">N</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel28.html#K3" title="WAYBEL28:func.3">lim_inf-Convergence</a> <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="txt" href="waybel28.html#E1:26"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="waybel28.html#D3" target="_self" title="WAYBEL28:def.3">Def3</a></i>;<br/>


</div>
