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

<b>let </b><font color="Maroon" title="c1">GX</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">A</font>, <font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">C</font>, <font color="Maroon" title="c5">D</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:4"/><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c3">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>and </b><br/><a NAME="E2:4"/><i><font color="Green" title="E8">A2</font></i>: 
<font color="Maroon" title="c4">C</font> <a href="connsp_1.html#R4" title="CONNSP_1:pred.4">is_a_component_of</a> <font color="Maroon" title="c5">D</font>
 <b>and </b><br/><a NAME="E3:4"/><i><font color="Green" title="E9">A3</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">C</font>
 <b>and </b><br/><a NAME="E4:4"/><i><font color="Green" title="E10">A4</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">B</font>
 <b>and </b><br/><a NAME="E5:4"/><i><font color="Green" title="E11">A5</font></i>: 
<font color="Maroon" title="c3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D</font>
 ;<br/>

<a NAME="E6:4"/><i><font color="Green" title="E12">A6</font></i>: 
( <font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="txt" href="goboard9.html#E4:4"><i><font color="Green" title="E10">A4</font></i></a>, <a class="ref" href="xboole_1.html#T65" title="XBOOLE_1:th.65">XBOOLE_1:65</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">A</font> = <font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c7">B</font> = <font color="Maroon" title="c3">B</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font> <b>by </b><i><a class="txt" href="goboard9.html#E4:4"><i><font color="Green" title="E10">A4</font></i></a>, <a class="ref" href="xboole_1.html#T65" title="XBOOLE_1:th.65">XBOOLE_1:65</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">C</font> = <font color="Maroon" title="c4">C</font>, <font color="Maroon" title="c9">D</font> = <font color="Maroon" title="c5">D</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font> <b>by </b><i><a class="txt" href="goboard9.html#E3:4"><i><font color="Green" title="E9">A3</font></i></a>, <a class="txt" href="goboard9.html#E5:4"><i><font color="Green" title="E11">A5</font></i></a>, <a class="txt" href="goboard9.html#E6:4"><i><font color="Green" title="E12">A6</font></i></a>, <a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">XBOOLE_1:3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">CC</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font><b> such that </b><br/><a NAME="E10:4"/><i><font color="Green" title="E13">A7</font></i>: 
<font color="Maroon" title="c10">CC</font> <a href="connsp_1.html#R4" title="CONNSP_1:pred.4">is_a_component_of</a> <font color="Maroon" title="c9">D</font>
 <b>and </b><br/><a NAME="E11:4"/><i><font color="Green" title="E14">A8</font></i>: 
<font color="Maroon" title="c7">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">CC</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:4"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="goboard9.html#E5:4"><i><font color="Green" title="E11">A5</font></i></a>, <a class="ref" href="goboard9.html#T5" target="_self" title="GOBOARD9:th.5">Th5</a></i>;<br/>
<a NAME="E12:4"/>
<font color="Maroon" title="c6">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c10">CC</font>
 
<b>by </b><i><a class="txt" href="goboard9.html#E4:4"><i><font color="Green" title="E10">A4</font></i></a>, <a class="txt" href="goboard9.html#E11:4"><i><font color="Green" title="E14">A8</font></i></a>, <a class="ref" href="xboole_1.html#T63" title="XBOOLE_1:th.63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E13:4"/><b>then </b><i><font color="Green" title="E15">A9</font></i>: 
<font color="Maroon" title="c8">C</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c10">CC</font>
 
<b>by </b><i><a class="txt" href="goboard9.html#E3:4"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="xboole_1.html#T63" title="XBOOLE_1:th.63">XBOOLE_1:63</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">C1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c9">D</font></span>)</span><b> such that </b><br/><a NAME="E15:4"/><i><font color="Green" title="E16">A10</font></i>: 
<font color="Maroon" title="c11">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">C</font>
 <b>and </b><br/><a NAME="E16:4"/><i><font color="Green" title="E17">A11</font></i>: 
<font color="Maroon" title="c11">C1</font> <a href="connsp_1.html#R3" title="CONNSP_1:pred.3">is_a_component_of</a> <font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c9">D</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:4"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="connsp_1.html#D6" title="CONNSP_1:def.6">CONNSP_1:def 6</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c12">CC1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c9">D</font></span>)</span><b> such that </b><br/><a NAME="E18:4"/><i><font color="Green" title="E18">A12</font></i>: 
<font color="Maroon" title="c12">CC1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">CC</font>
 <b>and </b><br/><a NAME="E19:4"/><i><font color="Green" title="E19">A13</font></i>: 
<font color="Maroon" title="c12">CC1</font> <a href="connsp_1.html#R3" title="CONNSP_1:pred.3">is_a_component_of</a> <font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c9">D</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E10:4"><i><font color="Green" title="E13">A7</font></i></a>, <a class="ref" href="connsp_1.html#D6" title="CONNSP_1:def.6">CONNSP_1:def 6</a></i>;<br/>
<b>thus </b><a NAME="E20:4"/>
<font color="Maroon" title="c3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">C</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E11:4"><i><font color="Green" title="E14">A8</font></i></a>, <a class="txt" href="goboard9.html#E13:4"><i><font color="Green" title="E15">A9</font></i></a>, <a class="txt" href="goboard9.html#E15:4"><i><font color="Green" title="E16">A10</font></i></a>, <a class="txt" href="goboard9.html#E16:4"><i><font color="Green" title="E17">A11</font></i></a>, <a class="txt" href="goboard9.html#E18:4"><i><font color="Green" title="E18">A12</font></i></a>, <a class="txt" href="goboard9.html#E19:4"><i><font color="Green" title="E19">A13</font></i></a>, <a class="ref" href="connsp_1.html#T37" title="CONNSP_1:th.37">CONNSP_1:37</a></i>;<br/>


</div>
