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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>assume </b><a NAME="E1:72"/><i><font color="Green" title="E47">A1</font></i>: 
<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/>

<b>hence </b><a NAME="E2:72"/>
<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</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="E3:72"/>
<span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</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="txt" href="cfunct_1.html#E1:72"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="cfunct_1.html#T84" target="_self" title="CFUNCT_1:th.84">Th84</a></i>;<br/>
<b>hence </b><a NAME="E4:72"/>
 <a href="valued_1.html#K31" title="VALUED_1:func.31">-</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="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a></i>;<br/>


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