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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:11"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="euclid.html#K3">abs</a> <font color="Maroon">F</font></span>)</span>
 <b>and </b><br/><a NAME="E2:11"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">i</font>
 ;<br/>

<a NAME="E3:11"/>
(  <a href="euclid.html#K3">abs</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <a href="euclid.html#K2">absreal</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">F</font> &amp; <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="euclid.html#K3">abs</a> <font color="Maroon">F</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E4:11"/><b>then </b>
<span class="p1">(<span class="default"><a href="euclid.html#K3">abs</a> <font color="Maroon">F</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <a href="euclid.html#K2">absreal</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">a</font>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<b>hence </b><a NAME="E5:11"/>
<span class="p1">(<span class="default"><a href="euclid.html#K3">abs</a> <font color="Maroon">F</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="euclid.html#D2">EUCLID:def 2</a></i>;<br/>


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