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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:104"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7" target="_self">NetUniv</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E2:104"/>
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K11" target="_self">Lim</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E4:104"/><i><font color="Green">E61</font></i>: 
not <font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#R1">is_eventually_in</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="yellow_6.html#D18" target="_self">Def18</a></i>;<br/>
<a NAME="E5:104"/>
<font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#R2">is_often_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="yellow_6.html#E4:104"><i><font color="Green">E61</font></i></a>, <a class="ref" href="waybel_0.html#T9">WAYBEL_0:9</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> as    <a href="yellow_6.html#M2" target="_self">subnet</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="yellow_6.html#T31" target="_self">Th31</a></i>;<br/>
<a NAME="E7:104"/><i><font color="Green">E62</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being <a href="waybel_0.html#V6">strict</a> <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></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">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="yellow_6.html#E1:104"><i><font color="Green">E60</font></i></a>, <a class="ref" href="yellow_6.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E8:104"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="waybel_0.html#R1">is_eventually_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#T32" target="_self">Th32</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<a NAME="E9:104"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E10:104"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="yellow_6.html#E7:104"><i><font color="Green">E62</font></i></a>, <a class="ref" href="classes1.html#D1">CLASSES1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E11:104"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7" target="_self">NetUniv</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="yellow_6.html#D14" target="_self">Def14</a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="yellow_6.html#M2" target="_self">subnet</a> of <font color="Maroon">c<sub>5</sub></font>;<br/>

<b>assume </b><a NAME="E12:104"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K11" target="_self">Lim</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E13:104"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="waybel_0.html#R1">is_eventually_in</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D18" target="_self">Def18</a></i>;<br/>
<a NAME="E14:104"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="waybel_0.html#R2">is_often_in</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#T28" target="_self">Th28</a></i>;<br/>
<a NAME="E15:104"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="waybel_0.html#R2">is_often_in</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E16:104"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow_6.html#E8:104"><i><font color="Green">E63</font></i></a>, <a class="ref" href="waybel_0.html#T10">WAYBEL_0:10</a></i>;<br/>


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