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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>consider </b><font color="Maroon" title="c3">Y0</font> being  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E2:7"/><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c2">D</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="c3">Y0</font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T10" title="TSEP_1:th.10">TSEP_1:10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">Y0</font> = <font color="Maroon" title="c3">Y0</font> as  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="tex_2.html#V2" title="TEX_2:attr.2">proper</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="tex_3.html#E2:7"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="tex_2.html#T13" title="TEX_2:th.13">TEX_2:13</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">Y0</font>
;<br/>

<b>thus </b><a NAME="E4:7"/>
<font color="Maroon" title="c2">D</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="c4">Y0</font>
 <b>by </b><i><a class="txt" href="tex_3.html#E2:7"><i><font color="Green" title="E7">A1</font></i></a></i>;<br/>


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