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<b>let </b><font color="Maroon" title="c2">X0</font> be    <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c3">A</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="tsp_2.html#E19"><i><font color="Green" title="E15">Lm1</font></i></a></i>;<br/>
<b>assume </b><a NAME="E2:21_8_1"/><i><font color="Green" title="E17">A13</font></i>: 
<font color="Maroon" title="c2">X0</font> is <a href="tex_2.html#V2" title="TEX_2:attr.2">proper</a>
 ;<br/>

<b>assume </b><a NAME="E3:21_8_1"/><i><font color="Green" title="E18">A14</font></i>: 
<font color="Maroon" title="c2">X0</font> is <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a>
 ;<br/>

<b>assume </b><a NAME="E4:21_8_1"/>
<font color="Maroon" title="c2">X0</font> is <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a>
 ;<br/>

<a NAME="E5:21_8_1"/><b>then </b><i><font color="Green" title="E19">A15</font></i>: 
<font color="Maroon" title="c3">A</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 
<b>by </b><i><a class="ref" href="tsep_1.html#T11" title="TSEP_1:th.11">TSEP_1:11</a></i>;<br/>
<a NAME="E6:21_8_1"/>
<font color="Maroon" title="c3">A</font> is <a href="tsp_2.html#V1" title="TSP_2:attr.1">maximal_T_0</a>
 
<b>by </b><i><a class="txt" href="tsp_2.html#E3:21_8_1"><i><font color="Green" title="E18">A14</font></i></a>, <a class="ref" href="tsp_2.html#T11" target="_self" title="TSP_2:th.11">Th11</a></i>;<br/>
<a NAME="E7:21_8_1"/><b>then </b>
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="txt" href="tsp_2.html#E5:21_8_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="tsp_2.html#T3" target="_self" title="TSP_2:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E8:21_8_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tsp_2.html#E2:21_8_1"><i><font color="Green" title="E17">A13</font></i></a>, <a class="ref" href="tex_2.html#T13" title="TEX_2:th.13">TEX_2:13</a></i>;<br/>


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