<?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">A1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">A2</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<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">B1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X0</font>;<br/><b>let </b><font color="Maroon">B2</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X0</font>;<br/>











<b>assume </b><a NAME="E1:28"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A1</font> &amp; <font color="Maroon">B2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font> )
 ;<br/>

<b>assume </b><a NAME="E2:28"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">A1</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A2</font>,<font color="Maroon">A2</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A1</font> <a href="connsp_1.html#R1">are_separated</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="tsep_1.html#D7">TSEP_1:def 7</a><br/>

<a NAME="E3:28"/>
( <font color="Maroon">B1</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">B2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A2</font></span>)</span> &amp; <font color="Maroon">B2</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A2</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A1</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="tsep_2.html#T9" target="_self">Th9</a>, <a class="ref" href="xboole_1.html#T50">XBOOLE_1:50</a></i>;<br/>
<a NAME="E4:28"/><b>then </b>
<font color="Maroon">B1</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">B2</font>,<font color="Maroon">B2</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">B1</font> <a href="connsp_1.html#R1">are_separated</a> 
 
<b>by </b><i><a class="ref" href="tsep_2.html#T10" target="_self">Th10</a>, <a class="ref" href="tsep_2.html#T5" target="_self">Th5</a></i>;<br/>
<b>hence </b><a NAME="E5:28"/>
<font color="Maroon">B1</font>,<font color="Maroon">B2</font> <a href="tsep_1.html#R2">are_weakly_separated</a> 
 <b>by </b><i><a class="ref" href="tsep_1.html#D7">TSEP_1:def 7</a></i>;<br/>


</div>
