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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>3</sub></font> as    <a href="yellow_6.html#M2">subnet</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="yellow_9.html#K1">incl</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> as    <a href="waybel21.html#M2" target="_self">Embedding</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="waybel21.html#T40" target="_self">Th40</a></i>;<br/>
<a NAME="E3:51"/>
<font color="Maroon">c<sub>4</sub></font> is  <a href="yellow_6.html#V2">full</a>  <a href="yellow_6.html#M1">SubNetStr</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_9.html#T14">WAYBEL_9:14</a></i>;<br/>
<a NAME="E4:51"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D9">YELLOW_6:def 9</a></i>;<br/>
<a NAME="E5:51"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_9.html#T13">WAYBEL_9:13</a></i>;<br/>
<a NAME="E6:51"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="yellow_9.html#K1">incl</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#D1">YELLOW_9:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>4</sub></font>;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E2:51_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="waybel_9.html#D7">WAYBEL_9:def 7</a></i>;<br/><b>assume </b><a NAME="E3:51_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E4:51_1"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="waybel21.html#E6:51"><i><font color="Green">E32</font></i></a>, <a class="txt" href="waybel21.html#E2:51_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>;<br/><a NAME="E5:51_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="waybel21.html#E2:51_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="yellow_0.html#D2">YELLOW_0:def 2</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="ref" href="waybel_9.html#D7">WAYBEL_9:def 7</a></i>;<br/><b>take </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>9</sub></font>;<br/><b>thus </b><a NAME="E7:51_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="waybel21.html#E4:51"><i><font color="Green">E31</font></i></a>, <a class="txt" href="waybel21.html#E2:51_1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="waybel21.html#E4:51_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E8:51_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="ref" href="waybel21.html#T36" target="_self">Th36</a></i>;<br/><b>hence </b><a NAME="E9:51_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="waybel21.html#E6:51"><i><font color="Green">E32</font></i></a>, <a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:51"/>
 <a href="waybel11.html#K1">lim_inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="waybel11.html#K1">lim_inf</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="waybel21.html#T38" target="_self">Th38</a></i>;<br/>


</div>
