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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">N</font> be   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">T</font>;<br/>



<b>assume </b><a NAME="E1:104"/><i><font color="Green" title="E60">A1</font></i>: 
<font color="Maroon" title="c2">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>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>;<br/>

<b>assume </b><a NAME="E2:104"/>
not <font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <font color="Maroon" title="c2">N</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">V</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c3">p</font><b> such that </b><br/><a NAME="E4:104"/><i><font color="Green" title="E61">A2</font></i>: 
not <font color="Maroon" title="c2">N</font> <a href="waybel_0.html#R1" title="WAYBEL_0:pred.1">is_eventually_in</a> <font color="Maroon" title="c4">V</font>
 <b>by </b><i><a class="ref" href="yellow_6.html#D18" target="_self" title="YELLOW_6:def.18">Def18</a></i>;<br/>
<a NAME="E5:104"/>
<font color="Maroon" title="c2">N</font> <a href="waybel_0.html#R2" title="WAYBEL_0:pred.2">is_often_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c4">V</font>
 
<b>by </b><i><a class="txt" href="yellow_6.html#E4:104"><i><font color="Green" title="E61">A2</font></i></a>, <a class="ref" href="waybel_0.html#T9" title="WAYBEL_0:th.9">WAYBEL_0:9</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">Y</font> = <font color="Maroon" title="c2">N</font> <a href="yellow_6.html#K6" title="YELLOW_6:func.6">"</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c4">V</font></span>)</span> as    <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Maroon" title="c2">N</font> <b>by </b><i><a class="ref" href="yellow_6.html#T31" target="_self" title="YELLOW_6:th.31">Th31</a></i>;<br/>
<a NAME="E7:104"/><i><font color="Green" title="E62">A3</font></i>: 
 ex <font color="Olive" title="b1">M</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">T</font> st <br/>( <font color="Olive" title="b1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">N</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">M</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">T</font> )
 
<b>by </b><i><a class="txt" href="yellow_6.html#E1:104"><i><font color="Green" title="E60">A1</font></i></a>, <a class="ref" href="yellow_6.html#D14" target="_self" title="YELLOW_6:def.14">Def14</a></i>;<br/>
<a NAME="E8:104"/><i><font color="Green" title="E63">A4</font></i>: 
<font color="Maroon" title="c5">Y</font> <a href="waybel_0.html#R1" title="WAYBEL_0:pred.1">is_eventually_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c4">V</font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#T32" target="_self" title="YELLOW_6:th.32">Th32</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">Y</font>
;<br/>

<a NAME="E9:104"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c2">N</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c4">V</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D13" target="_self" title="YELLOW_6:def.13">Def13</a></i>;<br/>
<a NAME="E10:104"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">Y</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">T</font>
 
<b>by </b><i><a class="txt" href="yellow_6.html#E7:104"><i><font color="Green" title="E62">A3</font></i></a>, <a class="ref" href="classes1.html#D1" title="CLASSES1:def.1">CLASSES1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E11:104"/>
<font color="Maroon" title="c5">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>
 <b>by </b><i><a class="ref" href="yellow_6.html#D14" target="_self" title="YELLOW_6:def.14">Def14</a></i>;<br/>

<b>let </b><font color="Maroon" title="c6">Z</font> be    <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Maroon" title="c5">Y</font>;<br/>

<b>assume </b><a NAME="E12:104"/>
<font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <font color="Maroon" title="c6">Z</font>
 ;<br/>

<a NAME="E13:104"/><b>then </b>
<font color="Maroon" title="c6">Z</font> <a href="waybel_0.html#R1" title="WAYBEL_0:pred.1">is_eventually_in</a> <font color="Maroon" title="c4">V</font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D18" target="_self" title="YELLOW_6:def.18">Def18</a></i>;<br/>
<a NAME="E14:104"/><b>then </b>
<font color="Maroon" title="c6">Z</font> <a href="waybel_0.html#R2" title="WAYBEL_0:pred.2">is_often_in</a> <font color="Maroon" title="c4">V</font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#T28" target="_self" title="YELLOW_6:th.28">Th28</a></i>;<br/>
<a NAME="E15:104"/><b>then </b>
<font color="Maroon" title="c5">Y</font> <a href="waybel_0.html#R2" title="WAYBEL_0:pred.2">is_often_in</a> <font color="Maroon" title="c4">V</font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#T27" target="_self" title="YELLOW_6:th.27">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" title="E63">A4</font></i></a>, <a class="ref" href="waybel_0.html#T10" title="WAYBEL_0:th.10">WAYBEL_0:10</a></i>;<br/>


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