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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>3</sub></font>, <a href="numbers.html#K2">COMPLEX</a> ;<br/>









<b>assume </b><a NAME="E1:86"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:86"/><b>then </b>
 <a href="comseq_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#T92" target="_self">Th92</a></i>;<br/>
<a NAME="E3:86"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="comseq_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="cfunct_1.html#E1:86"><i><font color="Green">E58</font></i></a>, <a class="ref" href="cfunct_1.html#T95" target="_self">Th95</a></i>;<br/>
<b>hence </b><a NAME="E4:86"/>
<font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="comseq_1.html#D10">COMSEQ_1:def 10</a></i>;<br/>

<a NAME="E5:86"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="cfunct_1.html#E1:86"><i><font color="Green">E58</font></i></a>, <a class="ref" href="cfunct_1.html#T93" target="_self">Th93</a></i>;<br/>
<b>hence </b><a NAME="E6:86"/>
<font color="Maroon">c<sub>5</sub></font> <a href="comseq_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="cfunct_1.html#E1:86"><i><font color="Green">E58</font></i></a>, <a class="ref" href="cfunct_1.html#T88" target="_self">Th88</a></i>;<br/>

<b>thus </b><a NAME="E7:86"/>
<font color="Maroon">c<sub>4</sub></font> <a href="comseq_1.html#K3">(#)</a> <font color="Maroon">c<sub>5</sub></font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="cfunct_1.html#E1:86"><i><font color="Green">E58</font></i></a>, <a class="txt" href="cfunct_1.html#E5:86"><i><font color="Green">E59</font></i></a>, <a class="ref" href="cfunct_1.html#T88" target="_self">Th88</a></i>;<br/>


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