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<b>let </b><font color="Maroon">seq</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:79"/>
<font color="Maroon">seq</font> is <a href="funct_1.html#V3">constant</a>
 ;<br/>

<b>then consider </b><font color="Maroon">r1</font> being  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E3:79"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">seq</font> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r1</font>
 <b>by </b><i/>;<br/>
<div><i><font color="Green">E33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">r</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon">p</font> = <font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r1</font>;<br/><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/><a NAME="E1:79_1_1"/>
<font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="txt" href="seqm_3.html#E10"><i><font color="Green">Lemma48</font></i></a></i>;<br/><b>hence </b><a NAME="E2:79_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="seq_1.html#K14">(#)</a> <font color="Maroon">seq</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="seq_1.html#T13">SEQ_1:13</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E2:79_1"/>
<font color="Maroon">r</font> <a href="seq_1.html#K14">(#)</a> <font color="Maroon">seq</font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:79"/>
for <font color="Olive">r</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  holds  <font color="Olive">r</font> <a href="seq_1.html#K14">(#)</a> <font color="Maroon">seq</font> is <a href="funct_1.html#V3">constant</a>
 ;<br/>

<a NAME="E6:79"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="seq_1.html#K14">(#)</a> <font color="Maroon">seq</font> is <a href="funct_1.html#V3">constant</a>
 
<b>by </b><i><a class="txt" href="seqm_3.html#E11"><i><font color="Green">Lemma49</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:79"/>
 <a href="seq_1.html#K17">-</a> <font color="Maroon">seq</font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i><a class="ref" href="seq_1.html#T25">SEQ_1:25</a></i>;<br/>

<b>take </b><font color="Maroon">p</font> =  <a href="complex1.html#K18">abs</a> <font color="Maroon">r1</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="seqm_3.html#D6" target="_self">SEQM_3:def 6</a><br/>

<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/>

<a NAME="E8:79"/>
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <font color="Maroon">r1</font>
 
<b>by </b><i><a class="txt" href="seqm_3.html#E10"><i><font color="Green">Lemma48</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:79"/>
<span class="p1">(<span class="default"><a href="seq_1.html#K22">abs</a> <font color="Maroon">seq</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="seq_1.html#T16">SEQ_1:16</a></i>;<br/>


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