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<b>let </b><font color="Maroon" title="c1">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">C</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c2">C</font>, <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon" title="c4">r</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ;<br/>







<b>assume </b><a NAME="E1:74"/>
<font color="Maroon" title="c3">f</font> <a href="cfunct_1.html#R1" title="CFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">Y</font>
 ;<br/>

<a NAME="E2:74"/><b>then </b>
<span class="p1"><a href="comseq_1.html#K9" title="COMSEQ_1:func.9">|.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="comseq_1.html#K9" title="COMSEQ_1:func.9">.|</a></span> <a href="rfunct_1.html#R3" title="RFUNCT_1:pred.3">is_bounded_on</a> <font color="Maroon" title="c1">Y</font>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#D3" target="_self" title="CFUNCT_1:def.3">Def3</a></i>;<br/>
<a NAME="E3:74"/><b>then </b>
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Maroon" title="c4">r</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="seq_1.html#K13" title="SEQ_1:func.13">(#)</a> <span class="p1"><a href="comseq_1.html#K9" title="COMSEQ_1:func.9">|.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="comseq_1.html#K9" title="COMSEQ_1:func.9">.|</a></span> <a href="rfunct_1.html#R3" title="RFUNCT_1:pred.3">is_bounded_on</a> <font color="Maroon" title="c1">Y</font>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T97" title="RFUNCT_1:th.97">RFUNCT_1:97</a></i>;<br/>
<a NAME="E4:74"/><b>then </b>
<span class="p1"><a href="comseq_1.html#K9" title="COMSEQ_1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">r</font> <a href="comseq_1.html#K4" title="COMSEQ_1:func.4">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span><a href="comseq_1.html#K9" title="COMSEQ_1:func.9">.|</a></span> <a href="rfunct_1.html#R3" title="RFUNCT_1:pred.3">is_bounded_on</a> <font color="Maroon" title="c1">Y</font>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#T39" target="_self" title="CFUNCT_1:th.39">Th39</a></i>;<br/>
<b>hence </b><a NAME="E5:74"/>
<font color="Maroon" title="c4">r</font> <a href="comseq_1.html#K4" title="COMSEQ_1:func.4">(#)</a> <font color="Maroon" title="c3">f</font> <a href="cfunct_1.html#R1" title="CFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">Y</font>
 <b>by </b><i><a class="ref" href="cfunct_1.html#D3" target="_self" title="CFUNCT_1:def.3">Def3</a></i>;<br/>


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