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<span class="kw">let </span><font color="Maroon" title="c2">X0</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">X0</font> is  <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>  implies  not <font color="Maroon" title="c2">X0</font> is  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">T_0</a>  )</span><br/>

<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T1" title="TSEP_1:th.1">TSEP_1:1</a></span>;<br/>
<a NAME="E2:45_1_1"/>
<font color="Maroon" title="c1">X</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T2" title="TSEP_1:th.2">TSEP_1:2</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T1" title="TSEP_1:th.1">TSEP_1:1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:45_1_1"/>
 not <font color="Maroon" title="c2">X0</font> is  <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c2">X0</font> is  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">T_0</a> </span><br/>

<a NAME="E5:45_1_1"/><span class="kw">then </span>
 not <font color="Maroon" title="c3">A0</font> is  <a href="subset_1.html#V1" title="SUBSET_1:attr.1">proper</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tex_2.html#T8" title="TEX_2:th.8">TEX_2:8</a></span>;<br/>
<a NAME="E6:45_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">A0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#D6" title="SUBSET_1:def.6">SUBSET_1:def 6</a></span>;<br/>
<a NAME="E7:45_1_1"/><span class="kw">then </span>
 not <font color="Maroon" title="c3">A0</font> is  <a href="tsp_1.html#V1" title="TSP_1:attr.1">T_0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsp_1.html#T4" target="_self" title="TSP_1:th.4">Th6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:45_1_1"/>
 not <font color="Maroon" title="c2">X0</font> is  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">T_0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsp_1.html#T13" target="_self" title="TSP_1:th.13">Th15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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