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<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>

<a NAME="E1:81"/><i><font color="Green">E33</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K2">COMPLEX</a>  <a href="finsop_1.html#K3">--&gt;</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K2">COMPLEX</a> 
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="81_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:81_1"/>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K2">COMPLEX</a> 
 <b>and </b><br/><a NAME="E2:81_1"/><i><font color="Green">E34</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">r</font>
 ;<br/><b>take </b><font color="Maroon">s</font> = <font color="Maroon">r</font>;<br/><b>thus </b><a NAME="E3:81_1"/>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">s</font>
 <b>by </b><i/>;<br/><b>let </b><font color="Maroon">x2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E4:81_1"/>
<font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K2">COMPLEX</a> 
 <b>and </b><br/><a NAME="E5:81_1"/>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x2</font> <a href="complex1.html#K11">-</a> <font color="Maroon">x1</font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">s</font>
 ;<br/><i><font color="Green">E38</font></i>: <span class="p1">(<span class="default"><a href="numbers.html#K2">COMPLEX</a>  <a href="finsop_1.html#K3">--&gt;</a> <font color="Maroon">x</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">x1</font> = 
<span class="p1">(<span class="default"><a href="numbers.html#K2">COMPLEX</a>  <a href="finsop_1.html#K3">--&gt;</a> <font color="Maroon">x</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x1</font>
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/><span class="p1">(<span class="default"><a href="numbers.html#K2">COMPLEX</a>  <a href="finsop_1.html#K3">--&gt;</a> <font color="Maroon">x</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">x2</font> = 
<span class="p1">(<span class="default"><a href="numbers.html#K2">COMPLEX</a>  <a href="finsop_1.html#K3">--&gt;</a> <font color="Maroon">x</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x2</font>
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/><b>hence </b><a NAME="E8:81_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"><span class="p4">(<span class="default"><a href="numbers.html#K2">COMPLEX</a>  <a href="finsop_1.html#K3">--&gt;</a> <font color="Maroon">x</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">x2</font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="numbers.html#K2">COMPLEX</a>  <a href="finsop_1.html#K3">--&gt;</a> <font color="Maroon">x</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">r</font>
 <b>by </b><i>, , <a class="ref" href="complex1.html#T130">COMPLEX1:130</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:81"/>
<a href="numbers.html#K2">COMPLEX</a>  <a href="finsop_1.html#K3">--&gt;</a> <font color="Maroon">x</font> <a href="cfcont_1.html#R2">is_continuous_on</a>  <a href="numbers.html#K2">COMPLEX</a> 
 <b>by </b><i>, <a class="ref" href="cfcont_1.html#T61">CFCONT_1:61</a></i>;<br/>


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