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

<b>let </b><font color="Maroon">FT1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">FT2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT1</font>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT2</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">FT1</font>,<font color="Maroon">FT2</font>;<br/>







<b>assume </b><a NAME="E1:17"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">A</font> is <a href="fin_topo.html#V5">connected</a> &amp; <font color="Maroon">f</font> <a href="fintopo4.html#R2" target="_self">is_continuous</a> 0 &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font> )
 ;<br/>

<a NAME="E2:17"/><b>then </b><i><font color="Green">E27</font></i>: 
for <font color="Olive">B1</font>, <font color="Olive">C1</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT1</font>  st <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Olive">B1</font> <a href="subset_1.html#K4">\/</a> <font color="Olive">C1</font> &amp; <font color="Olive">B1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">C1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">B1</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">C1</font> holds <br/><font color="Olive">B1</font> <a href="fin_topo.html#K9">^b</a>  <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Olive">C1</font>
 
<b>by </b><i><a class="ref" href="fin_topo.html#D18">FIN_TOPO:def 18</a></i>;<br/>
<a NAME="E3:17"/>
for <font color="Olive">B2</font>, <font color="Olive">C2</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT2</font>  st <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Olive">B2</font> <a href="subset_1.html#K4">\/</a> <font color="Olive">C2</font> &amp; <font color="Olive">B2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">C2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">B2</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">C2</font> holds <br/><font color="Olive">B2</font> <a href="fin_topo.html#K9">^b</a>  <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Olive">C2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">B2</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT2</font>, <font color="Maroon">C2</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT2</font>;<br/>

<b>assume </b><a NAME="E1:17_1"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B2</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">B2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">C2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">B2</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C2</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">B1</font> = <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">B2</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT1</font> ;<br/>
<a NAME="E3:17_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">B1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:17_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">B1</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:17_1_1"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<b>thus </b><a NAME="E4:17_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B2</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>


</div><b>end;</b></div>
<b>reconsider </b><font color="Maroon">B20</font> = <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">B1</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT2</font> ;<br/>
<a NAME="E5:17_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">B20</font> <a href="fin_topo.html#K9">^b</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">B2</font> <a href="fin_topo.html#K9">^b</a> 
 
<b>by </b><i>, <a class="ref" href="fin_topo.html#T19">FIN_TOPO:19</a></i>;<br/>
<b>reconsider </b><font color="Maroon">B10</font> = <font color="Maroon">B1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT1</font> ;<br/>
<b>reconsider </b><font color="Maroon">C1</font> = <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">C2</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT1</font> ;<br/>
<b>reconsider </b><font color="Maroon">C10</font> = <font color="Maroon">C1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT1</font> ;<br/>
<a NAME="E9:17_1"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">FT1</font>
 
;<br/>
<a NAME="E10:17_1"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E11:17_1"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">B2</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">C2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="relat_1.html#T175">RELAT_1:175</a></i>;<br/>
<a NAME="E12:17_1"/><b>then </b>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">C1</font>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T146">FUNCT_1:146</a></i>;<br/>
<a NAME="E13:17_1"/><b>then </b>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">C1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/>
<a NAME="E14:17_1"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B10</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">C10</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E15:17_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">B10</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E16:17_1"/>
<font color="Maroon">C10</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E17:17_1"/><b>then </b>
<font color="Maroon">B10</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">C10</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E18:17_1"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B10</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">C10</font>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E19:17_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">B10</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B1</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E20:17_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">C10</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E21:17_1"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">B10</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C10</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C1</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/>
<b>consider </b><font color="Maroon">x5</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">B2</font>;<br/>
<a NAME="E23:17_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">x5</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E24:17_1"/>
<font color="Maroon">x5</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>then consider </b><font color="Maroon">z5</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E26:17_1"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">z5</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">z5</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">x5</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z5</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<a NAME="E27:17_1"/>
<font color="Maroon">z5</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">B2</font>
 
<b>by </b><i>, <a class="ref" href="fintopo4.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>
<a NAME="E28:17_1"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">B10</font> <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="fintopo4.html#D1" target="_self">Def1</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon">x6</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C2</font>;<br/>
<a NAME="E30:17_1"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">x6</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E31:17_1"/>
<font color="Maroon">x6</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>then consider </b><font color="Maroon">z6</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E33:17_1"/><i><font color="Green">E74</font></i>: 
( <font color="Maroon">z6</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">z6</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">x6</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z6</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<a NAME="E34:17_1"/>
<font color="Maroon">z6</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">C2</font>
 
<b>by </b><i>, , <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>
<a NAME="E35:17_1"/><b>then </b><i><font color="Green">E75</font></i>: 
<font color="Maroon">C10</font> <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="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E36:17_1"/>
<font color="Maroon">B2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C2</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E37:17_1"/><b>then </b>
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><font color="Maroon">B2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T171">RELAT_1:171</a></i>;<br/>
<a NAME="E38:17_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">B2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">C2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="funct_1.html#T137">FUNCT_1:137</a></i>;<br/>
<a NAME="E39:17_1"/><b>then </b>
<font color="Maroon">B10</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C10</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E40:17_1"/><b>then </b>
<font color="Maroon">B10</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C10</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E41:17_1"/><b>then </b>
<font color="Maroon">B10</font> <a href="fin_topo.html#K9">^b</a>  <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">C10</font>
 
<b>by </b><i>, , <a class="ref" href="fintopo4.html#T1" target="_self">Th1</a>, <a class="txt" href="fintopo4.html#E1:17"><i><font color="Green">E25</font></i></a></i>;<br/>
<a NAME="E42:17_1"/><b>then </b><i><font color="Green">E76</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">B10</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C10</font> <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="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E43:17_1"/>
<font color="Maroon">B10</font> <a href="fin_topo.html#K9">^b</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> 
 
<b>by </b><i>, <a class="ref" href="fin_topo.html#T19">FIN_TOPO:19</a></i>;<br/>
<a NAME="E44:17_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">B10</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C10</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C1</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/>
<a NAME="E45:17_1"/><b>then </b><i><font color="Green">E77</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C1</font> <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="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E46:17_1"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">FT1</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E47:17_1"/><b>then </b><i><font color="Green">E78</font></i>: 
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C1</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="fintopo4.html#E2:17"><i><font color="Green">E27</font></i></a>, <a class="ref" href="relat_1.html#T152">RELAT_1:152</a></i>;<br/>
<a NAME="E48:17_1"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C1</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">C1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T154">RELAT_1:154</a></i>;<br/>
<a NAME="E49:17_1"/><b>then </b><i><font color="Green">E79</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">C1</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="fintopo4.html#E1:17_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E50:17_1"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">C1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C2</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T145">FUNCT_1:145</a></i>;<br/>
<a NAME="E51:17_1"/><b>then </b><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">C1</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T26">XBOOLE_1:26</a></i>;<br/>
<a NAME="E52:17_1"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">B20</font> <a href="fin_topo.html#K9">^b</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E53:17_1"/><b>then </b>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">B2</font> <a href="fin_topo.html#K9">^b</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E54:17_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C2</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">B2</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T26">XBOOLE_1:26</a></i>;<br/>
<a NAME="E55:17_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">C1</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">B2</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C2</font>
 
<b>by </b><i><a class="txt" href="fintopo4.html#E3:17_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E56:17_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">B2</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C2</font> <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="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<b>hence </b><a NAME="E57:17_1"/>
<font color="Maroon">B2</font> <a href="fin_topo.html#K9">^b</a>  <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">C2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:17"/>
<font color="Maroon">B</font> is <a href="fin_topo.html#V5">connected</a>
 <b>by </b><i><a class="ref" href="fin_topo.html#D18">FIN_TOPO:def 18</a></i>;<br/>


</div>
