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<b>let </b><font color="Maroon" title="c1">M</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="c2">V</font> be   <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</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="c1">M</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font>;<br/><b>let </b><font color="Maroon" title="c4">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>







<b>assume </b><a NAME="E1:60"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="partfun2.html#R1" title="PARTFUN2:pred.1">is_constant_on</a> <font color="Maroon" title="c4">Y</font>
 ;<br/>

<b>hence </b><a NAME="E2:60"/>
for <font color="Olive" title="b1">z</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a> holds  <font color="Olive" title="b1">z</font> <a href="vfunct_2.html#K4" title="VFUNCT_2:func.4">(#)</a> <font color="Maroon" title="c3">f</font> <a href="vfunct_2.html#R1" title="VFUNCT_2:pred.1">is_bounded_on</a> <font color="Maroon" title="c4">Y</font>
 <b>by </b><i><a class="ref" href="vfunct_2.html#T52" target="_self" title="VFUNCT_2:th.52">Th52</a>, <a class="ref" href="vfunct_2.html#T54" target="_self" title="VFUNCT_2:th.54">Th54</a></i>;<br/>

<a NAME="E3:60"/>
 <a href="vfunct_2.html#K6" title="VFUNCT_2:func.6">-</a> <font color="Maroon" title="c3">f</font> <a href="partfun2.html#R1" title="PARTFUN2:pred.1">is_constant_on</a> <font color="Maroon" title="c4">Y</font>
 
<b>by </b><i><a class="txt" href="vfunct_2.html#E1:60"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="vfunct_2.html#T53" target="_self" title="VFUNCT_2:th.53">Th53</a></i>;<br/>
<b>hence </b><a NAME="E4:60"/>
 <a href="vfunct_2.html#K6" title="VFUNCT_2:func.6">-</a> <font color="Maroon" title="c3">f</font> <a href="vfunct_2.html#R1" title="VFUNCT_2:pred.1">is_bounded_on</a> <font color="Maroon" title="c4">Y</font>
 <b>by </b><i><a class="ref" href="vfunct_2.html#T54" target="_self" title="VFUNCT_2:th.54">Th54</a></i>;<br/>

<a NAME="E5:60"/>
<span class="p1"><a href="vfunct_2.html#K5" title="VFUNCT_2:func.5">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="vfunct_2.html#K5" title="VFUNCT_2:func.5">.||</a></span> <a href="partfun2.html#R1" title="PARTFUN2:pred.1">is_constant_on</a> <font color="Maroon" title="c4">Y</font>
 
<b>by </b><i><a class="txt" href="vfunct_2.html#E1:60"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="vfunct_2.html#T53" target="_self" title="VFUNCT_2:th.53">Th53</a></i>;<br/>
<b>hence </b><a NAME="E6:60"/>
<span class="p1"><a href="vfunct_2.html#K5" title="VFUNCT_2:func.5">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="vfunct_2.html#K5" title="VFUNCT_2:func.5">.||</a></span> <a href="rfunct_1.html#R3" title="RFUNCT_1:pred.3">is_bounded_on</a> <font color="Maroon" title="c4">Y</font>
 <b>by </b><i><a class="ref" href="rfunct_1.html#T108" title="RFUNCT_1:th.108">RFUNCT_1:108</a></i>;<br/>


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