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<div class="add">

<b>let </b><font color="Maroon">q</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>

<b>thus </b><a NAME="E1:39"/>
( <font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies  <a href="finseq_1.html#K3" target="_self">len</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> 0 )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>assume </b><a NAME="E2:39_1"/>
 <a href="finseq_1.html#K3" target="_self">len</a> <font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E3:39_1"/><b>then </b>
 <a href="finseq_1.html#K3" target="_self">len</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2" target="_self">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" target="_self">len</a> <font color="Maroon">q</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:39_1"/><b>then </b>
 <a href="finseq_1.html#K3" target="_self">len</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4" target="_self">dom</a> <font color="Maroon">q</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:39_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" target="_self">len</a> <font color="Maroon">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" target="_self">len</a> <font color="Maroon">q</font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E6:39_1"/>
contradiction
 ;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:39"/>
 <a href="finseq_1.html#K3" target="_self">len</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E3:39"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="finseq_1.html#K4" target="_self">dom</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, </i>;<br/>
<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">q</font>;<br/>
<b>assume </b><a NAME="E5:39"/><i><font color="Green">E34</font></i>: 
not <font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">z</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:39"/><i><font color="Green">E35</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D1">RELAT_1:def 1</a></i>;<br/>
<b>thus </b><a NAME="E8:39"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="relat_1.html#D4">RELAT_1:def 4</a></i>;<br/>


</div>
