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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> 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="E1:79"/><i><font color="Green">E54</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>4</sub></font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:79"/><b>then </b><i><font color="Green">E55</font></i>: 
<span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="comseq_1.html#K9">.|</a></span> <a href="rfunct_1.html#R3">is_bounded_on</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E3:79"/>
<span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="comseq_1.html#K9">.|</a></span> <a href="rfunct_1.html#R3">is_bounded_on</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="cfunct_1.html#E1:79"><i><font color="Green">E54</font></i></a>, <a class="ref" href="cfunct_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E4:79"/><b>then </b>
<span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="comseq_1.html#K9">.|</a></span> <a href="rfunct_1.html#R3">is_bounded_on</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="cfunct_1.html#E2:79"><i><font color="Green">E55</font></i></a>, <a class="ref" href="rfunct_1.html#T104">RFUNCT_1:104</a></i>;<br/>
<b>hence </b><a NAME="E5:79"/>
<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#K2">\/</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="cfunct_1.html#D3" target="_self">Def3</a></i>;<br/>


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