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

<b>let </b><font color="Maroon">FMT</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="fintopo2.html#L1" target="_self">FMT_Space_Str</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>;<br/>



<b>assume </b><a NAME="E1:42"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font><br/> for <font color="Olive">V1</font>, <font color="Olive">V2</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>  st <font color="Olive">V1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> &amp; <font color="Olive">V2</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> holds <br/> ex <font color="Olive">W</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font> st <br/>( <font color="Olive">W</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> &amp; <font color="Olive">W</font> <a href="tarski.html#R1">c=</a> <font color="Olive">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Olive">V2</font> )
 ;<br/>

<a NAME="E2:42"/>
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span> <a href="fintopo2.html#K8" target="_self">^Fodelta</a>  holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fintopo2.html#K8" target="_self">^Fodelta</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fintopo2.html#K8" target="_self">^Fodelta</a> </span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font>;<br/>

<b>assume </b><a NAME="E1:42_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span> <a href="fintopo2.html#K8" target="_self">^Fodelta</a> 
 ;<br/>

<a NAME="E2:42_1"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">W1</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>  holds <br/>(  not <font color="Olive">W1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> or ( <font color="Olive">W1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> &amp; <font color="Olive">W1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  ) or ( <font color="Olive">W1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> &amp; <font color="Olive">W1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">W1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>;<br/>

<b>assume </b><a NAME="E1:42_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">W1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:42_1_1"/><b>then </b>
<font color="Maroon">W1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:42_1_1"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</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="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E4:42_1_1"/>
<font color="Maroon">W1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E5:42_1_1"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K3">`</a> </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="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E6:42_1_1"/><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</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="fintopo2.html#E1:42_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E7:42_1_1"/>
<font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K3">`</a> </span>)</span></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="ref" href="xboole_1.html#T53">XBOOLE_1:53</a></i>;<br/>
<a NAME="E8:42_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </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="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/>
<a NAME="E9:42_1_1"/><b>then </b><i><font color="Green">E38</font></i>: 
( <font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  &amp; <font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>then consider </b><font color="Maroon">z1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E11:42_1_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">z1</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K3">`</a> </span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#T4">XBOOLE_0:4</a></i>;<br/>
<b>consider </b><font color="Maroon">z2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E13:42_1_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">z2</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#T4">XBOOLE_0:4</a></i>;<br/>
<a NAME="E14:42_1_1"/>
( ( <font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  ) or ( <font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K3">`</a> </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="fintopo2.html#E2:42_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="fintopo2.html#T2" target="_self">Th2</a>, <a class="ref" href="fintopo2.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E15:42_1_1"/>
( ( <font color="Maroon">W1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> &amp; <font color="Maroon">W1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  ) or ( <font color="Maroon">W1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> &amp; <font color="Maroon">W1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  ) )
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:42_1"/>
for <font color="Olive">V1</font>, <font color="Olive">V2</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>  st <font color="Olive">V1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> &amp; <font color="Olive">V2</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> &amp; not <!--HUMANRECFAILED-->( <font color="Olive">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> &amp; <font color="Olive">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  ) holds <br/>( <font color="Olive">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> &amp; <font color="Olive">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">V1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>, <font color="Maroon">V2</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>;<br/>

<b>assume </b><a NAME="E1:42_1_2"/>
( <font color="Maroon">V1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> &amp; <font color="Maroon">V2</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> )
 ;<br/>

<b>then consider </b><font color="Maroon">W</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font><b> such that </b><br/><a NAME="E3:42_1_2"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">W</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E4:42_1_2"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">V2</font>
 <b>by </b><i/>;<br/>
<a NAME="E5:42_1_2"/>
( <font color="Maroon">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">V2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V1</font> &amp; <font color="Maroon">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">V2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V2</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E6:42_1_2"/><b>then </b>
( <font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V1</font> &amp; <font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V2</font> )
 
<b>by </b><i><a class="txt" href="fintopo2.html#E1:42_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E7:42_1_2"/><b>then </b><i><font color="Green">E75</font></i>: 
( <font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font> &amp; <font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">V1</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span> &amp; <font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> &amp; <font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">V2</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K3">`</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T26">XBOOLE_1:26</a></i>;<br/>
<a NAME="E8:42_1_2"/>
( ( <font color="Maroon">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> &amp; <font color="Maroon">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  ) or ( <font color="Maroon">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> &amp; <font color="Maroon">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_2_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:42_1_2_1_1_1"/>
( ( <font color="Maroon">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> &amp; <font color="Maroon">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  ) or ( <font color="Maroon">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> &amp; <font color="Maroon">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  ) )
 </span><b>by </b><i><a class="txt" href="fintopo2.html#E1:42"><i><font color="Green">E19</font></i></a>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_2_1_1_1_1"><b>case </b></a><a NAME="E1:42_1_2_1_1_1_1"/><i><font color="Green">E76</font></i>: 
( <font color="Maroon">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> &amp; <font color="Maroon">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  )
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">z1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:42_1_2_1_1_1_1"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">z1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#T4">XBOOLE_0:4</a></i>;<br/><b>consider </b><font color="Maroon">z2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:42_1_2_1_1_1_1"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">z2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span>
 <b>by </b><i><a class="txt" href="fintopo2.html#E2:42_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xboole_0.html#T4">XBOOLE_0:4</a></i>;<br/><b>thus </b><a NAME="E6:42_1_2_1_1_1_1"/>
( ( <font color="Maroon">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> &amp; <font color="Maroon">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  ) or ( <font color="Maroon">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> &amp; <font color="Maroon">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  ) )
 <b>by </b><i>, , <a class="ref" href="fintopo2.html#T2" target="_self">Th2</a>, <a class="ref" href="xboole_0.html#T4">XBOOLE_0:4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_2_1_1_1_2"><b>case </b></a><a NAME="E1:42_1_2_1_1_1_2"/><i><font color="Green">E79</font></i>: 
( <font color="Maroon">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> &amp; <font color="Maroon">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  )
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">z3</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:42_1_2_1_1_1_2"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">z3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#T4">XBOOLE_0:4</a></i>;<br/><b>consider </b><font color="Maroon">z4</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:42_1_2_1_1_1_2"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">z4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K3">`</a> </span>)</span>
 <b>by </b><i><a class="txt" href="fintopo2.html#E2:42_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xboole_0.html#T4">XBOOLE_0:4</a></i>;<br/><b>thus </b><a NAME="E6:42_1_2_1_1_1_2"/>
( ( <font color="Maroon">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> &amp; <font color="Maroon">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  ) or ( <font color="Maroon">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> &amp; <font color="Maroon">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  ) )
 <b>by </b><i>, , <a class="ref" href="fintopo2.html#T2" target="_self">Th2</a>, <a class="ref" href="xboole_0.html#T4">XBOOLE_0:4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:42_1_2_1"/>
( ( <font color="Maroon">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> &amp; <font color="Maroon">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  ) or ( <font color="Maroon">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> &amp; <font color="Maroon">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  ) )
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E9:42_1_2"/>
( ( <font color="Maroon">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> &amp; <font color="Maroon">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  ) or ( <font color="Maroon">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> &amp; <font color="Maroon">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  ) )
 ;<br/>


</div><b>end;</b></div>
<a NAME="E4:42_1"/><b>then </b>
( for <font color="Olive">V1</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>  st <font color="Olive">V1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> holds <br/>( <font color="Olive">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> &amp; <font color="Olive">V1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  ) or for <font color="Olive">V2</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>  st <font color="Olive">V2</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> holds <br/>( <font color="Olive">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> &amp; <font color="Olive">V2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  ) )
 
;<br/>
<a NAME="E5:42_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="fintopo2.html#K8" target="_self">^Fodelta</a>  or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> <a href="fintopo2.html#K8" target="_self">^Fodelta</a>  )
 
;<br/>
<b>hence </b><a NAME="E6:42_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fintopo2.html#K8" target="_self">^Fodelta</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fintopo2.html#K8" target="_self">^Fodelta</a> </span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:42"/>
<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span> <a href="fintopo2.html#K8" target="_self">^Fodelta</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fintopo2.html#K8" target="_self">^Fodelta</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fintopo2.html#K8" target="_self">^Fodelta</a> </span>)</span>
 <b>by </b><i><a class="ref" href="subset_1.html#T7">SUBSET_1:7</a></i>;<br/>


</div>
