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<b>let </b><font color="Maroon" title="c2">X0</font> be    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>assume </b><a NAME="E1:55_2_1"/><i><font color="Green" title="E17">A5</font></i>: 
not <font color="Maroon" title="c2">X0</font> is <a href="tsep_1.html#V1" title="TSEP_1:attr.1">open</a>
 ;<br/>

<b>assume </b><a NAME="E2:55_2_1"/>
not <font color="Maroon" title="c2">X0</font> is <a href="tex_2.html#V2" title="TEX_2:attr.2">proper</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E4:55_2_1"/><i><font color="Green" title="E18">A6</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font>
 <b>and </b><br/><a NAME="E5:55_2_1"/><i><font color="Green" title="E19">A7</font></i>: 
not <font color="Maroon" title="c3">A</font> is <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>
 <b>by </b><i><a class="ref" href="tex_2.html#D3" target="_self" title="TEX_2:def.3">Def3</a></i>;<br/>
<a NAME="E6:55_2_1"/><i><font color="Green" title="E20">A8</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="tex_2.html#E5:55_2_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="tex_2.html#T5" target="_self" title="TEX_2:th.5">Th5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/><b>assume </b><a NAME="E1:55_2_1_1"/>
<font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font>
 ;<br/><a NAME="E2:55_2_1_1"/><b>then </b>
<font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="tex_2.html#E4:55_2_1"><i><font color="Green" title="E18">A6</font></i></a>, <a class="txt" href="tex_2.html#E6:55_2_1"><i><font color="Green" title="E20">A8</font></i></a></i>;<br/><b>hence </b><a NAME="E3:55_2_1_1"/>
<font color="Maroon" title="c4">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:55_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_2.html#E1:55_2_1"><i><font color="Green" title="E17">A5</font></i></a>, <a class="ref" href="tsep_1.html#D1" title="TSEP_1:def.1">TSEP_1:def 1</a></i>;<br/>


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