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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="E1:79"/>
<font color="Maroon" title="c3">f</font> <a href="partfun2.html#R1" title="PARTFUN2:pred.1">is_constant_on</a> <font color="Maroon" title="c1">Y</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">r</font> being    <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> <b> such that </b><br/><a NAME="E3:79"/><i><font color="Green" title="E52">A1</font></i>: 
for <font color="Olive" title="b1">c</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">C</font>  st <font color="Olive" title="b1">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Y</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> holds <br/><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r</font>
 <b>by </b><i><a class="ref" href="partfun2.html#D3" title="PARTFUN2:def.3">PARTFUN2:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon" title="c5">p</font> = <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>;<br/><b>let </b><font color="Maroon" title="c6">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">C</font>;<br/><b>assume </b><a NAME="E1:79_1"/>
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Y</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E2:79_1"/>
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">p</font>
 <b>by </b><i><a class="txt" href="cfunct_1.html#E3:79"><i><font color="Green" title="E52">A1</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:79"/>
<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#T81" target="_self" title="CFUNCT_1:th.81">Th81</a></i>;<br/>


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