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

<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">Ns</font>, <font color="Maroon" title="c3">xs</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_1.html#D3" title="RELAT_1:def.3">RELAT_1:def 3</a><br/>



<a NAME="E1:32"/><i><font color="Green" title="E20">A1</font></i>: 
 <a href="waybel28.html#K3" title="WAYBEL28:func.3">lim_inf-Convergence</a> <font color="Maroon" title="c1">L</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c1">L</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D21" title="YELLOW_6:def.21">YELLOW_6:def 21</a></i>;<br/>
<b>assume </b><a NAME="E2:32"/><i><font color="Green" title="E21">A2</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">Ns</font>,<font color="Maroon" title="c3">xs</font></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>
 ;<br/>

<a NAME="E3:32"/><b>then </b>
<font color="Maroon" title="c2">Ns</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>
 
<b>by </b><i><a class="txt" href="waybel28.html#E1:32"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">N</font> being  <a href="waybel_0.html#V6" title="WAYBEL_0:attr.6">strict</a> <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E5:32"/><i><font color="Green" title="E22">A3</font></i>: 
<font color="Maroon" title="c4">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Ns</font>
 <b>and </b><br/><a NAME="E6:32"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K2" title="YELLOW_6:func.2">the_universe_of</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="ref" href="yellow_6.html#D14" title="YELLOW_6:def.14">YELLOW_6:def 14</a></i>;<br/>
<a NAME="E7:32"/><i><font color="Green" title="E23">A4</font></i>: 
<font color="Maroon" title="c4">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>
 
<b>by </b><i><a class="txt" href="waybel28.html#E1:32"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="waybel28.html#E2:32"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="waybel28.html#E5:32"><i><font color="Green" title="E22">A3</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">x</font> = <font color="Maroon" title="c3">xs</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="waybel28.html#E1:32"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="waybel28.html#E2:32"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E9:32"/>
<font color="Maroon" title="c4">N</font> is    <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Maroon" title="c4">N</font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#T23" title="YELLOW_6:th.23">YELLOW_6:23</a></i>;<br/>
<a NAME="E10:32"/><b>then </b>
<font color="Maroon" title="c5">x</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="Maroon" title="c4">N</font>
 
<b>by </b><i><a class="txt" href="waybel28.html#E2:32"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="waybel28.html#E5:32"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="waybel28.html#E7:32"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="waybel28.html#D3" target="_self" title="WAYBEL28:def.3">Def3</a></i>;<br/>
<a NAME="E11:32"/><b>then </b>
<font color="Maroon" title="c5">x</font> <a href="waybel11.html#R1" title="WAYBEL11:pred.1">is_S-limit_of</a> <font color="Maroon" title="c4">N</font>
 
<b>by </b><i><a class="ref" href="waybel11.html#D7" title="WAYBEL11:def.7">WAYBEL11:def 7</a></i>;<br/>
<b>hence </b><a NAME="E12:32"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">Ns</font>,<font color="Maroon" title="c3">xs</font></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="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="txt" href="waybel28.html#E5:32"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="waybel28.html#E7:32"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="waybel11.html#D8" title="WAYBEL11:def.8">WAYBEL11:def 8</a></i>;<br/>


</div>
