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<b>let </b><font color="Maroon" title="c2">Y0</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">Y</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">Y0</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">Y</font> <b>by </b><i><a class="txt" href="tex_2.html#E17"><i><font color="Green" title="E9">Lm1</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon" title="c4">A</font> = <font color="Maroon" title="c3">A</font>;<br/><b>thus </b><a NAME="E1:29_1_1_1"/>
( <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y0</font> &amp; not <font color="Maroon" title="c4">A</font> is <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:29_1_1"/>
not <font color="Maroon" title="c2">Y0</font> is <a href="tex_2.html#V2" title="TEX_2:attr.2">proper</a>
 <b>by </b><i><a class="ref" href="tex_2.html#D3" target="_self" title="TEX_2:def.3">Def3</a></i>;<br/>


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