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<b>let </b><font color="Maroon" title="c2">X0</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <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">A0</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <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="ref" href="tsep_1.html#T1" title="TSEP_1:th.1">TSEP_1:1</a></i>;<br/>
<a NAME="E2:46_2_1"/>
<font color="Maroon" title="c1">X</font> is    <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="tsep_1.html#T2" title="TSEP_1:th.2">TSEP_1:2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">A</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <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="ref" href="tsep_1.html#T1" title="TSEP_1:th.1">TSEP_1:1</a></i>;<br/>
<b>assume </b><a NAME="E4:46_2_1"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c2">X0</font> is <a href="t_0topsp.html#V2" title="T_0TOPSP:attr.2">T_0</a>
 ;<br/>

<b>assume </b><a NAME="E5:46_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/>

<a NAME="E6:46_2_1"/><b>then </b>
not <font color="Maroon" title="c3">A0</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#T13" title="TEX_2:th.13">TEX_2:13</a></i>;<br/>
<a NAME="E7:46_2_1"/><b>then </b>
<font color="Maroon" title="c3">A0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font>
 
<b>by </b><i><a class="ref" href="tex_2.html#T5" title="TEX_2:th.5">TEX_2:5</a></i>;<br/>
<a NAME="E8:46_2_1"/><b>then </b>
not <font color="Maroon" title="c3">A0</font> is <a href="tsp_1.html#V1" title="TSP_1:attr.1">T_0</a>
 
<b>by </b><i><a class="ref" href="tsp_1.html#T6" target="_self" title="TSP_1:th.6">Th6</a></i>;<br/>
<b>hence </b><a NAME="E9:46_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tsp_1.html#E4:46_2_1"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="tsp_1.html#T15" target="_self" title="TSP_1:th.15">Th15</a></i>;<br/>


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