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<b>let </b><font color="Maroon">Y0</font> be  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>assume </b><a NAME="E1:32_1_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">Y0</font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font>;<br/><b>assume </b><a NAME="E1:32_1_1_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font>
 ;<br/><b>then reconsider </b><font color="Maroon">B</font> = <font color="Maroon">A</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font> ;<br/><b>reconsider </b><font color="Maroon">B</font> = <font color="Maroon">B</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="realset1.html#V1">trivial</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font> <b>by </b><i>, , <a class="ref" href="realset2.html#D5">REALSET2:def 5</a></i>;<br/><a NAME="E4:32_1_1_1"/>
<font color="Maroon">B</font> is <a href="tex_2.html#V1" target="_self">proper</a>
 ;<br/><b>hence </b><a NAME="E5:32_1_1_1"/>
<font color="Maroon">A</font> is <a href="tex_2.html#V1" target="_self">proper</a>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:32_1_1"/>
<font color="Maroon">Y0</font> is <a href="tex_2.html#V2" target="_self">proper</a>
 <b>by </b><i/>;<br/>


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