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<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>;<br/>





<b>assume </b><a NAME="E1:50"/><i><font color="Green" title="E44">A1</font></i>: 
( <font color="Maroon" title="c3">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> )
 ;<br/>

<a NAME="E2:50"/><b>then </b><i><font color="Green" title="E45">A2</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">f</font>
 
<b>by </b><i><a class="ref" href="finseq_6.html#T46" target="_self" title="FINSEQ_6:th.46">Th46</a></i>;<br/>
<a NAME="E3:50"/>
<font color="Maroon" title="c2">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="finseq_6.html#E1:50"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="finseq_6.html#T47" target="_self" title="FINSEQ_6:th.47">Th47</a></i>;<br/>
<a NAME="E4:50"/><b>then </b><i><font color="Green" title="E46">A3</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="finseq_4.html#K5" title="FINSEQ_4:func.5">-|</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="finseq_6.html#E2:50"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="finseq_4.html#T52" title="FINSEQ_4:th.52">FINSEQ_4:52</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c3">f</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <font color="Maroon" title="c2">p</font> = 
<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
<b>by </b><i><a class="txt" href="finseq_6.html#E2:50"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="finseq_6.html#T44" target="_self" title="FINSEQ_6:th.44">Th44</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>
;<br/><br/>

<b>thus </b><font color="Maroon" title="c3">f</font> = 
<span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="finseq_4.html#K6" title="FINSEQ_4:func.6">|--</a> <font color="Maroon" title="c2">p</font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E2:50"><i><font color="Green" title="E45">A2</font></i></a>, <a class="txt" href="finseq_6.html#E4:50"><i><font color="Green" title="E46">A3</font></i></a>, <a class="ref" href="finseq_4.html#T66" title="FINSEQ_4:th.66">FINSEQ_4:66</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="finseq_4.html#K6" title="FINSEQ_4:func.6">|--</a> <font color="Maroon" title="c2">p</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="finseq_5.html#K2" title="FINSEQ_5:func.2">:-</a> <font color="Maroon" title="c2">p</font>
<b>by </b><i><a class="txt" href="finseq_6.html#E2:50"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="finseq_6.html#T45" target="_self" title="FINSEQ_6:th.45">Th45</a></i>
;<br/>


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