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<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">N</font> be   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/>





<b>assume </b><a NAME="E1:103"/>
not <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>
 ;<br/>

<b>then consider </b><font color="Maroon">V</font> being    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">p</font><b> such that </b><br/><a NAME="E3:103"/><i><font color="Green">E29</font></i>: 
not <font color="Maroon">N</font> <a href="waybel_0.html#R1">is_eventually_in</a> <font color="Maroon">V</font>
 <b>by </b><i/>;<br/>
<a NAME="E4:103"/>
<font color="Maroon">N</font> <a href="waybel_0.html#R2">is_often_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D5" target="_self">Def5</a>, <a class="ref" href="waybel_0.html#T9">WAYBEL_0:9</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">Y</font> = <font color="Maroon">N</font> <a href="yellow_6.html#K6" target="_self">"</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span> as    <a href="yellow_6.html#M2" target="_self">subnet</a> of <font color="Maroon">N</font> <b>by </b><i/>;<br/>
<a NAME="E6:103"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">Y</font> <a href="waybel_0.html#R1">is_eventually_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font>
 
<b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">Y</font>
;<br/>

<b>let </b><font color="Maroon">Z</font> be    <a href="yellow_6.html#M2" target="_self">subnet</a> of <font color="Maroon">Y</font>;<br/>

<b>assume </b><a NAME="E7:103"/>
<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">Z</font>
 ;<br/>

<a NAME="E8:103"/><b>then </b>
<font color="Maroon">Z</font> <a href="waybel_0.html#R1">is_eventually_in</a> <font color="Maroon">V</font>
 
<b>by </b><i/>;<br/>
<a NAME="E9:103"/><b>then </b>
<font color="Maroon">Z</font> <a href="waybel_0.html#R2">is_often_in</a> <font color="Maroon">V</font>
 
<b>by </b><i/>;<br/>
<a NAME="E10:103"/><b>then </b>
<font color="Maroon">Y</font> <a href="waybel_0.html#R2">is_often_in</a> <font color="Maroon">V</font>
 
<b>by </b><i><a class="txt" href="yellow_6.html#E6:103"><i><font color="Green">E32</font></i></a></i>;<br/>
<b>hence </b><a NAME="E11:103"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow_6.html#E16"><i><font color="Green">Lemma60</font></i></a>, <a class="ref" href="waybel_0.html#T10">WAYBEL_0:10</a></i>;<br/>


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