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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">Y1</font>, <font color="Maroon" title="c3">Y2</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>;<br/>





<b>reconsider </b><font color="Maroon" title="c4">A1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y1</font>, <font color="Maroon" title="c5">A2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">Y2</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1" title="TSEP_1:th.1">TSEP_1:1</a></i>;<br/>
<b>assume </b><a NAME="E2:6"/>
<font color="Maroon" title="c2">Y1</font>,<font color="Maroon" title="c3">Y2</font> <a href="tsep_2.html#R4" title="TSEP_2:pred.4">constitute_a_decomposition</a> 
 ;<br/>

<a NAME="E3:6"/><b>then </b>
<font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c5">A2</font> <a href="tsep_2.html#R2" title="TSEP_2:pred.2">constitute_a_decomposition</a> 
 
<b>by </b><i><a class="ref" href="tsep_2.html#D2" title="TSEP_2:def.2">TSEP_2:def 2</a></i>;<br/>
<a NAME="E4:6"/><b>then </b>
( <font color="Maroon" title="c4">A1</font> is <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> &amp; <font color="Maroon" title="c5">A2</font> is <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> )
 
<b>by </b><i><a class="ref" href="tex_3.html#T1" target="_self" title="TEX_3:th.1">Th1</a></i>;<br/>
<b>hence </b><a NAME="E5:6"/>
( <font color="Maroon" title="c2">Y1</font> is <a href="tex_2.html#V2" title="TEX_2:attr.2">proper</a> &amp; <font color="Maroon" title="c3">Y2</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#T13" title="TEX_2:th.13">TEX_2:13</a></i>;<br/>


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