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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="sprect_1.html#V1" target="_self">rectangular</a> <a href="struct_0.html#NM8">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>

<a NAME="E1:117"/><i><font color="Green">E87</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="sprect_1.html#D3" target="_self">Def3</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E3:117"/><i><font color="Green">E88</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E4:117"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E5:117"/>
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:117"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="connsp_1.html#R4">is_a_component_of</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>and </b><br/><a NAME="E7:117"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="connsp_1.html#R4">is_a_component_of</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="sprect_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E8:117"/><i><font color="Green">E92</font></i>: 
 <a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">c<sub>1</sub></font> <a href="connsp_1.html#R4">is_a_component_of</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="goboard9.html#D1">GOBOARD9:def 1</a></i>;<br/>
<a NAME="E9:117"/><i><font color="Green">E93</font></i>: 
 <a href="goboard9.html#K3">RightComp</a> <font color="Maroon">c<sub>1</sub></font> <a href="connsp_1.html#R4">is_a_component_of</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="goboard9.html#D2">GOBOARD9:def 2</a></i>;<br/>
<a NAME="E10:117"/>
<span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="gobrd12.html#T11">GOBRD12:11</a></i>;<br/>
<a NAME="E11:117"/><b>then </b>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="txt" href="sprect_1.html#E1:117"><i><font color="Green">E87</font></i></a>, <a class="txt" href="sprect_1.html#E3:117"><i><font color="Green">E88</font></i></a>, <a class="txt" href="sprect_1.html#E6:117"><i><font color="Green">E90</font></i></a>, <a class="txt" href="sprect_1.html#E7:117"><i><font color="Green">E91</font></i></a>, <a class="txt" href="sprect_1.html#E8:117"><i><font color="Green">E92</font></i></a>, <a class="txt" href="sprect_1.html#E9:117"><i><font color="Green">E93</font></i></a>, <a class="ref" href="sprect_1.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E12:117"/><b>then </b>
( (  <a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="goboard9.html#K3">RightComp</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> ) or (  <a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="goboard9.html#K3">RightComp</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> ) )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T10">ZFMISC_1:10</a></i>;<br/>
<b>hence </b><a NAME="E13:117"/>
 <a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="goboard9.html#K3">RightComp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="sprect_1.html#E4:117"><i><font color="Green">E89</font></i></a></i>;<br/>


</div>
