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

<b>let </b><font color="Maroon" title="c1">GX</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">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> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font>;<br/><b>let </b><font color="Maroon" title="c3">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">GX</font>;<br/>





<b>assume </b><a NAME="E1:23"/><i><font color="Green" title="E18">A1</font></i>: 
( <font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c2">A</font> is    <a href="connsp_3.html#M1" title="CONNSP_3:mode.1">a_union_of_components</a> of <font color="Maroon" title="c1">GX</font> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">F</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">GX</font><b> such that </b><br/><a NAME="E3:23"/><i><font color="Green" title="E19">A2</font></i>: 
( ( for <font color="Olive" title="b1">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font>  st <font color="Olive" title="b1">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> holds <br/><font color="Olive" title="b1">B</font> <a href="connsp_1.html#R3" title="CONNSP_1:pred.3">is_a_component_of</a> <font color="Maroon" title="c1">GX</font> ) &amp; <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c4">F</font> )
 <b>by </b><i><a class="ref" href="connsp_3.html#D2" target="_self" title="CONNSP_3:def.2">Def2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">X</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:23"/><i><font color="Green" title="E20">A3</font></i>: 
( <font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X</font> &amp; <font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> )
 <b>by </b><i><a class="txt" href="connsp_3.html#E1:23"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="connsp_3.html#E3:23"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">B2</font> = <font color="Maroon" title="c5">X</font> as   <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="connsp_3.html#E5:23"><i><font color="Green" title="E20">A3</font></i></a></i>;<br/>
<a NAME="E7:23"/>
<font color="Maroon" title="c6">B2</font> <a href="connsp_1.html#R3" title="CONNSP_1:pred.3">is_a_component_of</a> <font color="Maroon" title="c1">GX</font>
 
<b>by </b><i><a class="txt" href="connsp_3.html#E3:23"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="connsp_3.html#E5:23"><i><font color="Green" title="E20">A3</font></i></a></i>;<br/>
<a NAME="E8:23"/><b>then </b>
<font color="Maroon" title="c6">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Maroon" title="c3">p</font>
 
<b>by </b><i><a class="txt" href="connsp_3.html#E5:23"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="connsp_1.html#T44" title="CONNSP_1:th.44">CONNSP_1:44</a></i>;<br/>
<b>hence </b><a NAME="E9:23"/>
 <a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Maroon" title="c3">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="connsp_3.html#E3:23"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="connsp_3.html#E5:23"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="zfmisc_1.html#T92" title="ZFMISC_1:th.92">ZFMISC_1:92</a></i>;<br/>


</div>
