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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> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">A1</font>, <font color="Maroon" title="c3">A2</font>, <font color="Maroon" title="c4">C1</font>, <font color="Maroon" title="c5">C2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>assume </b><a NAME="E1:19"/><i><font color="Green" title="E14">A1</font></i>: 
( <font color="Maroon" title="c2">A1</font>,<font color="Maroon" title="c4">C1</font> <a href="tsep_2.html#R2" title="TSEP_2:pred.2">constitute_a_decomposition</a>  &amp; <font color="Maroon" title="c3">A2</font>,<font color="Maroon" title="c5">C2</font> <a href="tsep_2.html#R2" title="TSEP_2:pred.2">constitute_a_decomposition</a>  )
 ;<br/>

<a NAME="E2:19"/><b>then </b><i><font color="Green" title="E15">A2</font></i>: 
( <font color="Maroon" title="c2">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  &amp; <font color="Maroon" title="c3">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C2</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )
 
<b>by </b><i><a class="ref" href="tsep_2.html#T4" target="_self" title="TSEP_2:th.4">Th4</a></i>;<br/>
<b>assume </b><a NAME="E3:19"/>
<font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">C2</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="c1">X</font>
 ;<br/>

<a NAME="E4:19"/><b>then </b>
<font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">X</font>
 
;<br/>
<a NAME="E5:19"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">C2</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>;<br/>
<a NAME="E6:19"/><b>then </b>
<font color="Maroon" title="c2">A1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="tsep_2.html#E2:19"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="xboole_1.html#T53" title="XBOOLE_1:th.53">XBOOLE_1:53</a></i>;<br/>
<a NAME="E7:19"/><b>then </b><i><font color="Green" title="E16">A3</font></i>: 
<font color="Maroon" title="c2">A1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">A2</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<b>assume </b><a NAME="E8:19"/>
<font color="Maroon" title="c4">C1</font>,<font color="Maroon" title="c5">C2</font> <a href="tsep_1.html#R2" title="TSEP_1:pred.2">are_weakly_separated</a> 
 ;<br/>

<b>hence </b><a NAME="E9:19"/>
<font color="Maroon" title="c2">A1</font>,<font color="Maroon" title="c3">A2</font> <a href="connsp_1.html#R1" title="CONNSP_1:pred.1">are_separated</a> 
 <b>by </b><i><a class="txt" href="tsep_2.html#E1:19"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="tsep_2.html#E7:19"><i><font color="Green" title="E16">A3</font></i></a>, <a class="ref" href="tsep_2.html#T19" target="_self" title="TSEP_2:th.19">Th19</a></i>;<br/>


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