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<b>let </b><font color="Maroon" title="c1">f</font> be  <a href="seq_1.html#NV1" title="SEQ_1:NV.1">real-yielding</a> <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/>

<b>set </b><font color="Maroon" title="c2">n</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">x</font> = <font color="Maroon" title="c1">f</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <b>by </b><i><a class="txt" href="euclid.html#E13"><i><font color="Green" title="E5">Lm2</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:17_1"/>
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span>
 ;<br/><b>reconsider </b><font color="Maroon" title="c5">r</font> = <font color="Maroon" title="c1">f</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">j</font>, <font color="Maroon" title="c6">r'</font> = <span class="p1">(<span class="default"><a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">j</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="euclid.html#K10" title="EUCLID:func.10">abs</a> <span class="p2">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">j</font> = 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <font color="Maroon" title="c6">r'</font>
<b>by </b><i><a class="ref" href="euclid.html#T6" target="_self" title="EUCLID:th.6">Th6</a></i>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c5">r</font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T35" title="RVSUM_1:th.35">RVSUM_1:35</a></i>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <font color="Maroon" title="c5">r</font>
<b>by </b><i><a class="ref" href="complex1.html#T138" title="COMPLEX1:th.138">COMPLEX1:138</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="euclid.html#K10" title="EUCLID:func.10">abs</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">j</font>
<b>by </b><i><a class="ref" href="euclid.html#T6" target="_self" title="EUCLID:th.6">Th6</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:17"/>
 <a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T139" title="FINSEQ_2:th.139">FINSEQ_2:139</a></i>;<br/>


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