<?xml version="1.0"?>
<div class="add">

<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">X0</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>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>;<br/>





<b>assume </b><a NAME="E1:46"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">X1</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X0</font> &amp; <font color="Maroon">X2</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X0</font> )
 ;<br/>

<b>let </b><font color="Maroon">Y1</font> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X0</font>, <font color="Maroon">Y2</font> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X0</font>;<br/>

<b>assume </b><a NAME="E2:46"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">Y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X1</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X0</font> &amp; <font color="Maroon">Y2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X2</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X0</font> )
 ;<br/>

<b>assume </b><a NAME="E3:46"/>
<font color="Maroon">X1</font>,<font color="Maroon">X2</font> <a href="tsep_1.html#R3">are_separated</a> 
 ;<br/>

<a NAME="E4:46"/><b>then </b>
<font color="Maroon">X1</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X0</font>,<font color="Maroon">X2</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X0</font> <a href="tsep_1.html#R3">are_separated</a> 
 
<b>by </b><i>, <a class="ref" href="tsep_1.html#T76">TSEP_1:76</a></i>;<br/>
<b>hence </b><a NAME="E5:46"/>
<font color="Maroon">Y1</font>,<font color="Maroon">Y2</font> <a href="tsep_1.html#R3">are_separated</a> 
 <b>by </b><i><a class="ref" href="tsep_2.html#T19" target="_self">Th19</a>, </i>;<br/>


</div>
