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<b>let </b><font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">y</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y</font>;<br/>



<b>assume </b><a NAME="E1:46"/><i><font color="Green">E17</font></i>: 
 <a href="tex_2.html#K1" target="_self">Sspace</a> <font color="Maroon">y</font> is <a href="tex_2.html#V2" target="_self">proper</a>
 ;<br/>

<b>assume </b><a NAME="E2:46"/>
<font color="Maroon">Y</font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">Y</font> = <font color="Maroon">Y</font> as  non <a href="struct_0.html#V3">empty</a> <a href="realset2.html#V3">trivial</a>  <a href="pre_topc.html#L1">TopStruct</a>  ;<br/>
<a NAME="E4:46"/>
 <a href="tex_2.html#K1" target="_self">Sspace</a> <font color="Maroon">y</font> is  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">Y</font>
 
;<br/>
<b>hence </b><a NAME="E5:46"/>
contradiction
 <b>by </b><i><a class="ref" href="tex_2.html#D1" target="_self">Def1</a></i>;<br/>


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