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<b>let </b><font color="Maroon">M</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="clvect_1.html#NM5">ComplexNormSpace</a>;<br/><b>let </b><font color="Maroon">f1</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">M</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">f2</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">M</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>











<b>assume </b><a NAME="E1:62"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">f1</font> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">X</font> &amp; <font color="Maroon">f2</font> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">Y</font> )
 ;<br/>

<a NAME="E2:62"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">f2</font> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="vfunct_2.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E3:62"/><b>then </b>
(  <a href="vfunct_2.html#K6" target="_self">-</a> <font color="Maroon">f1</font> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">X</font> &amp;  <a href="vfunct_2.html#K6" target="_self">-</a> <font color="Maroon">f2</font> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">Y</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:62"/><b>then </b>
( <font color="Maroon">f1</font> <a href="vfunct_2.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><a href="vfunct_2.html#K6" target="_self">-</a> <font color="Maroon">f2</font></span>)</span> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">f2</font> <a href="vfunct_2.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><a href="vfunct_2.html#K6" target="_self">-</a> <font color="Maroon">f1</font></span>)</span> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">Y</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X</font> )
 
<b>by </b><i>, <a class="txt" href="vfunct_2.html#E1:62"><i><font color="Green">E27</font></i></a>, </i>;<br/>
<b>hence </b><a NAME="E5:62"/>
( <font color="Maroon">f1</font> <a href="vfunct_2.html#K2" target="_self">-</a> <font color="Maroon">f2</font> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">f2</font> <a href="vfunct_2.html#K2" target="_self">-</a> <font color="Maroon">f1</font> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font> )
 <b>by </b><i/>;<br/>


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