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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/>





<b>assume </b><a NAME="E1:50"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> )
 ;<br/>

<a NAME="E2:50"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:50"/>
<font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_6.html#T5" target="_self">Th5</a>, </i>;<br/>
<a NAME="E4:50"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">f</font> <a href="finseq_4.html#K6">-|</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="finseq_6.html#T6" target="_self">Th6</a>, <a class="ref" href="finseq_4.html#T52">FINSEQ_4:52</a></i>;<br/>
<b>hence </b><font color="Maroon">f</font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">p</font> = 
<a href="xboole_0.html#K1">{}</a>  <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">p</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_6.html#T6" target="_self">Th6</a>, </i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">p</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>
;<br/><br/>

<b>thus </b><font color="Maroon">f</font> = 
<span class="p1">(<span class="default"><a href="xboole_0.html#K1">{}</a>  <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">p</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_4.html#K7">|--</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_6.html#T6" target="_self">Th6</a>, <a class="ref" href="finseq_6.html#T7" target="_self">Th7</a>, <a class="ref" href="finseq_4.html#T66">FINSEQ_4:66</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">p</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_4.html#K7">|--</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">p</font>
<b>by </b><i><a class="ref" href="finseq_6.html#T6" target="_self">Th6</a>, </i>
;<br/>


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