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<b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">C</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">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>, <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon">r</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>







<b>assume </b><a NAME="E1:74"/>
<font color="Maroon">f</font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E2:74"/><b>then </b>
<span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">f</font></span><a href="comseq_1.html#K9">.|</a></span> <a href="rfunct_1.html#R3">is_bounded_on</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E3:74"/><b>then </b>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">r</font></span><a href="complex1.html#K17">.|</a></span> <a href="seq_1.html#K13">(#)</a> <span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">f</font></span><a href="comseq_1.html#K9">.|</a></span> <a href="rfunct_1.html#R3">is_bounded_on</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T97">RFUNCT_1:97</a></i>;<br/>
<a NAME="E4:74"/><b>then </b>
<span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="comseq_1.html#K4">(#)</a> <font color="Maroon">f</font></span>)</span></span><a href="comseq_1.html#K9">.|</a></span> <a href="rfunct_1.html#R3">is_bounded_on</a> <font color="Maroon">Y</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:74"/>
<font color="Maroon">r</font> <a href="comseq_1.html#K4">(#)</a> <font color="Maroon">f</font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T16" target="_self">Th16</a></i>;<br/>


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