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<b>let </b><font color="Maroon">it1</font> be    <a href="yellow_6.html#M4" target="_self">Convergence-Class</a> of <font color="Maroon">T</font>, <font color="Maroon">it2</font> be    <a href="yellow_6.html#M4" target="_self">Convergence-Class</a> of <font color="Maroon">T</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:108_1_2"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">N</font> being  <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">T</font><br/> for <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">N</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">it1</font> iff ( <font color="Olive">N</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7" target="_self">NetUniv</a> <font color="Maroon">T</font> &amp; <font color="Olive">p</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K11" target="_self">Lim</a> <font color="Olive">N</font> ) )
 <b>and </b><br/><a NAME="E2:108_1_2"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">N</font> being  <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">T</font><br/> for <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">N</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">it2</font> iff ( <font color="Olive">N</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7" target="_self">NetUniv</a> <font color="Maroon">T</font> &amp; <font color="Olive">p</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K11" target="_self">Lim</a> <font color="Olive">N</font> ) )
 ;<br/>

<a NAME="E3:108_1_2"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">it1</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_6.html#K7" target="_self">NetUniv</a> <font color="Maroon">T</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:108_1_2"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">it2</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_6.html#K7" target="_self">NetUniv</a> <font color="Maroon">T</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i/>;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_1.html#D2">RELAT_1:def 2</a><br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>thus </b><a NAME="E5:108_1_2"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">it1</font> implies <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">it2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="108_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:108_1_2_1"/><i><font color="Green">E117</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">it1</font>
 ;<br/>

<a NAME="E2:108_1_2_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7" target="_self">NetUniv</a> <font color="Maroon">T</font>
 
<b>by </b><i><a class="txt" href="yellow_6.html#E17"><i><font color="Green">Lemma64</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>then consider </b><font color="Maroon">N</font> being  <a href="waybel_0.html#V6">strict</a> <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E4:108_1_2_1"/><i><font color="Green">E118</font></i>: 
<font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E5:108_1_2_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K2" target="_self">the_universe_of</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">p</font> = <font color="Maroon">y</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> <b>by </b><i><a class="txt" href="yellow_6.html#E17"><i><font color="Green">Lemma64</font></i></a>, , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E7:108_1_2_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">N</font>,<font color="Maroon">p</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">it1</font>
 
<b>by </b><i>, <a class="ref" href="yellow_6.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E8:108_1_2_1"/><b>then </b>
( <font color="Maroon">N</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7" target="_self">NetUniv</a> <font color="Maroon">T</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K11" target="_self">Lim</a> <font color="Maroon">N</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E9:108_1_2_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">it2</font>
 <b>by </b><i>, <a class="ref" href="yellow_6.html#T11" target="_self">Th11</a></i>;<br/>


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

<b>assume </b><a NAME="E6:108_1_2"/><i><font color="Green">E119</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">it2</font>
 ;<br/>

<a NAME="E7:108_1_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7" target="_self">NetUniv</a> <font color="Maroon">T</font>
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>then consider </b><font color="Maroon">N</font> being  <a href="waybel_0.html#V6">strict</a> <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E9:108_1_2"/><i><font color="Green">E127</font></i>: 
<font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E10:108_1_2"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K2" target="_self">the_universe_of</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">p</font> = <font color="Maroon">y</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E12:108_1_2"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">N</font>,<font color="Maroon">p</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">it2</font>
 
<b>by </b><i>, <a class="ref" href="yellow_6.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E13:108_1_2"/><b>then </b>
( <font color="Maroon">N</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7" target="_self">NetUniv</a> <font color="Maroon">T</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K11" target="_self">Lim</a> <font color="Maroon">N</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E14:108_1_2"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">it1</font>
 <b>by </b><i>, <a class="ref" href="yellow_6.html#T11" target="_self">Th11</a></i>;<br/>


</div>
