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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>, <font color="Maroon">c<sub>4</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>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>











<b>assume </b><a NAME="E1:53"/><i><font color="Green">E23</font></i>: 
( <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>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<a NAME="E2:53"/><b>then </b>
 <a href="vfunct_2.html#K6" target="_self">-</a> <font color="Maroon">c<sub>4</sub></font> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="vfunct_2.html#T45" target="_self">Th45</a></i>;<br/>
<a NAME="E3:53"/><b>then </b>
<font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></font></span>)</span> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="vfunct_2.html#E1:53"><i><font color="Green">E23</font></i></a>, <a class="ref" href="vfunct_2.html#T46" target="_self">Th46</a></i>;<br/>
<b>hence </b><a NAME="E4:53"/>
<font color="Maroon">c<sub>3</sub></font> <a href="vfunct_2.html#K2" target="_self">-</a> <font color="Maroon">c<sub>4</sub></font> <a href="vfunct_2.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="vfunct_2.html#T25" target="_self">Th25</a></i>;<br/>


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