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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">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">H</font> be    <a href="seqfunc.html#M1" target="_self">Functional_Sequence</a> of <font color="Maroon">D</font>, <a href="numbers.html#K1">REAL</a> ;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="seqfunc.html#K5" target="_self">abs</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="seqfunc.html#K2" target="_self">(#)</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">n</font> = 
 <a href="seq_1.html#K21">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="seqfunc.html#K2" target="_self">(#)</a> <font color="Maroon">H</font></span>)</span> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="seq_1.html#K21">abs</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="seq_1.html#K13">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">H</font> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <font color="Maroon">r</font></span>)</span> <a href="seq_1.html#K13">(#)</a> <span class="p1">(<span class="default"><a href="seq_1.html#K21">abs</a> <span class="p2">(<span class="default"><font color="Maroon">H</font> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T37">RFUNCT_1:37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <font color="Maroon">r</font></span>)</span> <a href="seq_1.html#K13">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="seqfunc.html#K5" target="_self">abs</a> <font color="Maroon">H</font></span>)</span> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18">abs</a> <font color="Maroon">r</font></span>)</span> <a href="seqfunc.html#K2" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="seqfunc.html#K5" target="_self">abs</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="seqfunc.html#K1" target="_self">.</a> <font color="Maroon">n</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:30"/>
 <a href="seqfunc.html#K5" target="_self">abs</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="seqfunc.html#K2" target="_self">(#)</a> <font color="Maroon">H</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <font color="Maroon">r</font></span>)</span> <a href="seqfunc.html#K2" target="_self">(#)</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K5" target="_self">abs</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i/>;<br/>


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