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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">V</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c2">C</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">V</font>;<br/>







<b>assume </b><a NAME="E1:60"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="partfun2.html#R1" title="PARTFUN2:pred.1">is_constant_on</a> <font color="Maroon" title="c1">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" title="c5">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><a NAME="E1:60_1"/>
<font color="Maroon" title="c5">r</font> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Maroon" title="c4">f</font> <a href="partfun2.html#R1" title="PARTFUN2:pred.1">is_constant_on</a> <font color="Maroon" title="c1">Y</font>
 <b>by </b><i><a class="txt" href="vfunct_1.html#E1:60"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="vfunct_1.html#T59" target="_self" title="VFUNCT_1:th.59">Th59</a></i>;<br/><b>hence </b><a NAME="E2:60_1"/>
<font color="Maroon" title="c5">r</font> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Maroon" title="c4">f</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">Y</font>
 <b>by </b><i><a class="ref" href="vfunct_1.html#T61" target="_self" title="VFUNCT_1:th.61">Th61</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:60"/>
for <font color="Olive" title="b1">r</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds  <font color="Olive" title="b1">r</font> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Maroon" title="c4">f</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">Y</font>
 ;<br/>

<a NAME="E4:60"/>
 <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Maroon" title="c4">f</font> <a href="partfun2.html#R1" title="PARTFUN2:pred.1">is_constant_on</a> <font color="Maroon" title="c1">Y</font>
 
<b>by </b><i><a class="txt" href="vfunct_1.html#E1:60"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="vfunct_1.html#T60" target="_self" title="VFUNCT_1:th.60">Th60</a></i>;<br/>
<b>hence </b><a NAME="E5:60"/>
 <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Maroon" title="c4">f</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">Y</font>
 <b>by </b><i><a class="ref" href="vfunct_1.html#T61" target="_self" title="VFUNCT_1:th.61">Th61</a></i>;<br/>

<a NAME="E6:60"/>
<span class="p1"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">||.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">.||</a></span> <a href="partfun2.html#R1" title="PARTFUN2:pred.1">is_constant_on</a> <font color="Maroon" title="c1">Y</font>
 
<b>by </b><i><a class="txt" href="vfunct_1.html#E1:60"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="vfunct_1.html#T60" target="_self" title="VFUNCT_1:th.60">Th60</a></i>;<br/>
<b>hence </b><a NAME="E7:60"/>
<span class="p1"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">||.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">.||</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="rfunct_1.html#T108" title="RFUNCT_1:th.108">RFUNCT_1:108</a></i>;<br/>


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