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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">X1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>, <font color="Maroon">X2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>, <font color="Maroon">Y1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>, <font color="Maroon">Y2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>



<b>assume </b><a NAME="E1:41"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">X1</font>,<font color="Maroon">Y1</font> <a href="tsep_2.html#R4" target="_self">constitute_a_decomposition</a>  &amp; <font color="Maroon">X2</font>,<font color="Maroon">Y2</font> <a href="tsep_2.html#R4" target="_self">constitute_a_decomposition</a>  )
 ;<br/>

<b>assume </b><a NAME="E2:41"/>
<font color="Maroon">Y1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">Y2</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">X</font> #)
 ;<br/>

<a NAME="E3:41"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">X1</font> <a href="tsep_1.html#R1">misses</a> <font color="Maroon">X2</font>
 
<b>by </b><i>, <a class="ref" href="tsep_2.html#T14" target="_self">Th14</a></i>;<br/>
<b>assume </b><a NAME="E4:41"/>
<font color="Maroon">Y1</font>,<font color="Maroon">Y2</font> <a href="tsep_1.html#R4">are_weakly_separated</a> 
 ;<br/>

<b>hence </b><a NAME="E5:41"/>
<font color="Maroon">X1</font>,<font color="Maroon">X2</font> <a href="tsep_1.html#R3">are_separated</a> 
 <b>by </b><i>, , <a class="ref" href="tsep_2.html#T16" target="_self">Th16</a></i>;<br/>


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