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<b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">C</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">V</font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>;<br/>







<b>assume </b><a NAME="E1:60"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">f</font> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">Y</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">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/><a NAME="E1:60_1"/>
<font color="Maroon">r</font> <a href="vfunct_1.html#K4" target="_self">(#)</a> <font color="Maroon">f</font> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">Y</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E2:60_1"/>
<font color="Maroon">r</font> <a href="vfunct_1.html#K4" target="_self">(#)</a> <font color="Maroon">f</font> <a href="vfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">Y</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:60"/>
for <font color="Olive">r</font> being  <a href="real_1.html#NM1">Real</a> holds  <font color="Olive">r</font> <a href="vfunct_1.html#K4" target="_self">(#)</a> <font color="Maroon">f</font> <a href="vfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E4:60"/>
 <a href="vfunct_1.html#K6" target="_self">-</a> <font color="Maroon">f</font> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:60"/>
 <a href="vfunct_1.html#K6" target="_self">-</a> <font color="Maroon">f</font> <a href="vfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">Y</font>
 <b>by </b><i/>;<br/>

<a NAME="E6:60"/>
<span class="p1"><a href="vfunct_1.html#K5" target="_self">||.</a><span class="default"><font color="Maroon">f</font></span><a href="vfunct_1.html#K5" target="_self">.||</a></span> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E7:60"/>
<span class="p1"><a href="vfunct_1.html#K5" target="_self">||.</a><span class="default"><font color="Maroon">f</font></span><a href="vfunct_1.html#K5" target="_self">.||</a></span> <a href="rfunct_1.html#R3">is_bounded_on</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="rfunct_1.html#T108">RFUNCT_1:108</a></i>;<br/>


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