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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="clvect_1.html#NM5">ComplexNormSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:60"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="cfunct_1.html#NM1">Complex</a>;<br/><a NAME="E1:60_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="vfunct_2.html#K4" target="_self">(#)</a> <font color="Maroon">c<sub>3</sub></font> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="vfunct_2.html#E1:60"><i><font color="Green">E26</font></i></a>, <a class="ref" href="vfunct_2.html#T52" target="_self">Th52</a></i>;<br/><b>hence </b><a NAME="E2:60_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="vfunct_2.html#K4" target="_self">(#)</a> <font color="Maroon">c<sub>3</sub></font> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="vfunct_2.html#T54" target="_self">Th54</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:60"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="cfunct_1.html#NM1">Complex</a> holds <font color="Olive">b<sub>1</sub></font> <a href="vfunct_2.html#K4" target="_self">(#)</a> <font color="Maroon">c<sub>3</sub></font> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E4:60"/>
 <a href="vfunct_2.html#K6" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="vfunct_2.html#E1:60"><i><font color="Green">E26</font></i></a>, <a class="ref" href="vfunct_2.html#T53" target="_self">Th53</a></i>;<br/>
<b>hence </b><a NAME="E5:60"/>
 <a href="vfunct_2.html#K6" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="vfunct_2.html#T54" target="_self">Th54</a></i>;<br/>

<a NAME="E6:60"/>
<span class="p1"><a href="vfunct_2.html#K5" target="_self">||.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="vfunct_2.html#K5" target="_self">.||</a></span> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="vfunct_2.html#E1:60"><i><font color="Green">E26</font></i></a>, <a class="ref" href="vfunct_2.html#T53" target="_self">Th53</a></i>;<br/>
<b>hence </b><a NAME="E7:60"/>
<span class="p1"><a href="vfunct_2.html#K5" target="_self">||.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="vfunct_2.html#K5" target="_self">.||</a></span> <a href="rfunct_1.html#R3">is_bounded_on</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="rfunct_1.html#T108">RFUNCT_1:108</a></i>;<br/>


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