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<b>let </b><font color="Maroon" title="c1">seq</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:32"/>
<font color="Maroon" title="c1">seq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">r</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E3:32"/><i><font color="Green" title="E25">A1</font></i>: 
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">seq</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font>
 <b>by </b><i><a class="ref" href="seqm_3.html#D6" title="SEQM_3:def.6">SEQM_3:def 6</a></i>;<br/>
<b>take </b><font color="Maroon" title="c3">g</font> = <font color="Maroon" title="c2">r</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="seq_2.html#D6" title="SEQ_2:def.6">SEQ_2:def 6</a><br/>

<b>let </b><font color="Maroon" title="c4">p</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>assume </b><a NAME="E4:32"/><i><font color="Green" title="E26">A2</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">p</font>
 ;<br/>

<b>take </b><font color="Maroon" title="c5">n</font> =  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>

<b>let </b><font color="Maroon" title="c6">m</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E5:32"/>
<font color="Maroon" title="c5">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">m</font>
 ;<br/>

 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c6">m</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">g</font></span>)</span> = 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">g</font></span>)</span>
<b>by </b><i><a class="txt" href="seq_4.html#E3:32"><i><font color="Green" title="E25">A1</font></i></a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="absvalue.html#T7" title="ABSVALUE:th.7">ABSVALUE:7</a></i>
;<br/>
<b>hence </b><a NAME="E7:32"/>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c6">m</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">p</font>
 <b>by </b><i><a class="txt" href="seq_4.html#E4:32"><i><font color="Green" title="E26">A2</font></i></a></i>;<br/>


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