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<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>



<b>assume </b><a NAME="E1:17"/><i><font color="Green">E12</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:17"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="comseq_2.html#V2" target="_self">convergent</a>
 
<b>by </b><i><a class="ref" href="comseq_2.html#T9" target="_self">Th9</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">c<sub>4</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>assume </b><a NAME="E1:17_1"/><i><font color="Green">E14</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><b>take </b><font color="Maroon">c<sub>5</sub></font> = 0;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E2:17_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E3:17_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="comseq_2.html#E1:17"><i><font color="Green">E12</font></i></a></i>;<br/><b>hence </b><a NAME="E4:17_1"/>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="comseq_2.html#E1:17_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="complex1.html#T130">COMPLEX1:130</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:17"/>
 <a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="comseq_2.html#E2:17"><i><font color="Green">E13</font></i></a>, <a class="ref" href="comseq_2.html#D5" target="_self">Def5</a></i>;<br/>


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