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<div class="add">

<b>reconsider </b><font color="Maroon" title="c2">C</font> = <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">T</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> as    <a href="yellow_6.html#M4" title="YELLOW_6:mode.4">Convergence-Class</a> of <font color="Maroon" title="c1">T</font> <b>by </b><i><a class="ref" href="yellow_6.html#D21" target="_self" title="YELLOW_6:def.21">Def21</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">C</font>
;<br/>

<b>thus </b><a NAME="E2:116_1_1"/>
not <font color="Maroon" title="c2">C</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/>

<b>thus </b><a NAME="E3:116_1_1"/>
<font color="Maroon" title="c2">C</font> is <a href="yellow_6.html#V8" title="YELLOW_6:attr.8">topological</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="116_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:116_1_1_1"/>
<font color="Maroon" title="c2">C</font> is <a href="yellow_6.html#V4" title="YELLOW_6:attr.4">(CONSTANTS)</a>
  <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_6.html#D28" target="_self" title="YELLOW_6:def.28">YELLOW_6:def 28</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="116_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">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">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_6.html#D23" target="_self" title="YELLOW_6:def.23">YELLOW_6:def 23</a><br/>

<b>thus </b><a NAME="E1:116_1_1_1_1"/>
( <font color="Maroon" title="c3">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">T</font> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">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="c3">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> <font color="Maroon" title="c2">C</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:116_1_1_1"/>
<font color="Maroon" title="c2">C</font> is <a href="yellow_6.html#V5" title="YELLOW_6:attr.5">(SUBNETS)</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="116_1_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">N</font> be   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_6.html#D24" target="_self" title="YELLOW_6:def.24">YELLOW_6:def 24</a><br/><b>let </b><font color="Maroon" title="c4">Y</font> be    <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Maroon" title="c3">N</font>;<br/>



<b>thus </b><a NAME="E1:116_1_1_1_2"/>
( <font color="Maroon" title="c4">Y</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">T</font> implies for <font color="Olive" title="b1">p</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">N</font>,<font color="Olive" title="b1">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">Y</font>,<font color="Olive" title="b1">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:116_1_1_1"/>
<font color="Maroon" title="c2">C</font> is <a href="yellow_6.html#V6" title="YELLOW_6:attr.6">(DIVERGENCE)</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="116_1_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">X</font> be   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_6.html#D25" target="_self" title="YELLOW_6:def.25">YELLOW_6:def 25</a><br/><b>let </b><font color="Maroon" title="c4">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>;<br/>



<b>thus </b><a NAME="E1:116_1_1_1_3"/>
( <font color="Maroon" title="c3">X</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">T</font> &amp; not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> implies  ex <font color="Olive" title="b1">Y</font> being   <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Maroon" title="c3">X</font> st <br/>( <font color="Olive" title="b1">Y</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">T</font> &amp; ( for <font color="Olive" title="b2">Z</font> being   <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Olive" title="b1">Y</font>  holds not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">Z</font>,<font color="Maroon" title="c4">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> ) ) )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c3">X</font> be   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_6.html#D26" target="_self" title="YELLOW_6:def.26">YELLOW_6:def 26</a><br/><b>let </b><font color="Maroon" title="c4">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>;<br/>



<b>assume </b><a NAME="E4:116_1_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font>
 ;<br/>

<a NAME="E5:116_1_1_1"/><b>then </b><i><font color="Green" title="E67">A1</font></i>: 
<font color="Maroon" title="c3">X</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">T</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>let </b><font color="Maroon" title="c5">J</font> be    <a href="yellow_6.html#M3" title="YELLOW_6:mode.3">net_set</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font>;<br/>

<b>assume </b><a NAME="E6:116_1_1_1"/><i><font color="Green" title="E68">A2</font></i>: 
for <font color="Olive" title="b1">i</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">X</font> holds  <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">J</font> <a href="yellow_6.html#K8" title="YELLOW_6:func.8">.</a> <font color="Olive" title="b1">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</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> <font color="Maroon" title="c2">C</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="116_1_1_1_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">i</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">X</font>;<br/><a NAME="E1:116_1_1_1_4"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">J</font> <a href="yellow_6.html#K8" title="YELLOW_6:func.8">.</a> <font color="Maroon" title="c6">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c6">i</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> <font color="Maroon" title="c2">C</font>
 <b>by </b><i><a class="txt" href="yellow_6.html#E6:116_1_1_1"><i><font color="Green" title="E68">A2</font></i></a></i>;<br/><b>hence </b><a NAME="E2:116_1_1_1_4"/>
<font color="Maroon" title="c5">J</font> <a href="yellow_6.html#K8" title="YELLOW_6:func.8">.</a> <font color="Maroon" title="c6">i</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">T</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/></div><b>end;</b></div>
<a NAME="E8:116_1_1_1"/><b>then </b>
 <a href="yellow_6.html#K9" title="YELLOW_6:func.9">Iterated</a> <font color="Maroon" title="c5">J</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">T</font>
 
<b>by </b><i><a class="txt" href="yellow_6.html#E5:116_1_1_1"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="yellow_6.html#T34" target="_self" title="YELLOW_6:th.34">Th34</a></i>;<br/>
<b>hence </b><a NAME="E9:116_1_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_6.html#K9" title="YELLOW_6:func.9">Iterated</a> <font color="Maroon" title="c5">J</font></span>)</span>,<font color="Maroon" title="c4">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>


</div><b>end;</b></div>


</div>
