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<b>let </b><font color="Maroon" title="c1">T</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="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">T</font>;<br/><b>let </b><font color="Maroon" title="c3">i</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font>;<br/>





<b>reconsider </b><font color="Maroon" title="c4">M</font> = <font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K6" title="WAYBEL_9:func.6">|</a> <font color="Maroon" title="c3">i</font> as    <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Maroon" title="c2">N</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">e</font> =  <a href="yellow_9.html#K1" title="YELLOW_9:func.1">incl</a> <font color="Maroon" title="c4">M</font>,<font color="Maroon" title="c2">N</font> as    <a href="waybel21.html#M2" title="WAYBEL21:mode.2">Embedding</a> of <font color="Maroon" title="c4">M</font>,<font color="Maroon" title="c2">N</font> <b>by </b><i><a class="ref" href="waybel21.html#T40" target="_self" title="WAYBEL21:th.40">Th40</a></i>;<br/>
<a NAME="E3:51"/>
<font color="Maroon" title="c4">M</font> is  <a href="yellow_6.html#V2" title="YELLOW_6:attr.2">full</a>  <a href="yellow_6.html#M1" title="YELLOW_6:mode.1">SubNetStr</a> of <font color="Maroon" title="c2">N</font>
 
<b>by </b><i><a class="ref" href="waybel_9.html#T14" title="WAYBEL_9:th.14">WAYBEL_9:14</a></i>;<br/>
<a NAME="E4:51"/><b>then </b><i><font color="Green" title="E31">A1</font></i>: 
<font color="Maroon" title="c4">M</font> is  <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>  <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c2">N</font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D9" title="YELLOW_6:def.9">YELLOW_6:def 9</a></i>;<br/>
<a NAME="E5:51"/><i><font color="Green" title="E32">A2</font></i>: 
 <a href="yellow_9.html#K1" title="YELLOW_9:func.1">incl</a> <font color="Maroon" title="c4">M</font>,<font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">M</font>
 
<b>by </b><i><a class="ref" href="waybel_9.html#T13" title="WAYBEL_9:th.13">WAYBEL_9:13</a>, <a class="ref" href="yellow_9.html#D1" title="YELLOW_9:def.1">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" title="c6">k</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font>;<br/><b>let </b><font color="Maroon" title="c7">j</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">M</font>;<br/><b>consider </b><font color="Maroon" title="c8">j'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font><b> such that </b><br/><a NAME="E2:51_1"/><i><font color="Green" title="E33">A3</font></i>: 
( <font color="Maroon" title="c8">j'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">j</font> &amp; <font color="Maroon" title="c8">j'</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c3">i</font> )
 <b>by </b><i><a class="ref" href="waybel_9.html#D7" title="WAYBEL_9:def.7">WAYBEL_9:def 7</a></i>;<br/><b>assume </b><a NAME="E3:51_1"/>
<font color="Maroon" title="c5">e</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c7">j</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 ;<br/><a NAME="E4:51_1"/><b>then </b><i><font color="Green" title="E34">A4</font></i>: 
<font color="Maroon" title="c6">k</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c8">j'</font>
 <b>by </b><i><a class="txt" href="waybel21.html#E5:51"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="waybel21.html#E2:51_1"><i><font color="Green" title="E33">A3</font></i></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>;<br/><a NAME="E5:51_1"/><b>then </b>
<font color="Maroon" title="c6">k</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c3">i</font>
 <b>by </b><i><a class="txt" href="waybel21.html#E2:51_1"><i><font color="Green" title="E33">A3</font></i></a>, <a class="ref" href="yellow_0.html#D2" title="YELLOW_0:def.2">YELLOW_0:def 2</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c9">k'</font> = <font color="Maroon" title="c6">k</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">M</font> <b>by </b><i><a class="ref" href="waybel_9.html#D7" title="WAYBEL_9:def.7">WAYBEL_9:def 7</a></i>;<br/><b>take </b><font color="Maroon" title="c10">k'</font> = <font color="Maroon" title="c9">k'</font>;<br/><b>thus </b><a NAME="E7:51_1"/>
<font color="Maroon" title="c10">k'</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="txt" href="waybel21.html#E4:51"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="waybel21.html#E2:51_1"><i><font color="Green" title="E33">A3</font></i></a>, <a class="txt" href="waybel21.html#E4:51_1"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E8:51_1"/>
( <font color="Maroon" title="c4">M</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c10">k'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">e</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c10">k'</font></span>)</span> &amp; <font color="Maroon" title="c4">M</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c10">k'</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">M</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c10">k'</font> )
 <b>by </b><i><a class="ref" href="waybel21.html#T36" target="_self" title="WAYBEL21:th.36">Th36</a></i>;<br/><b>hence </b><a NAME="E9:51_1"/>
<font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c6">k</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c4">M</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c10">k'</font>
 <b>by </b><i><a class="txt" href="waybel21.html#E5:51"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:51"/>
 <a href="waybel11.html#K1" title="WAYBEL11:func.1">lim_inf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K6" title="WAYBEL_9:func.6">|</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel11.html#K1" title="WAYBEL11:func.1">lim_inf</a> <font color="Maroon" title="c2">N</font>
 <b>by </b><i><a class="ref" href="waybel21.html#T38" target="_self" title="WAYBEL21:th.38">Th38</a></i>;<br/>


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