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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:25"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="bhsp_3.html#V2" target="_self">bounded</a>
 <b>and </b><br/><a NAME="E2:25"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="bhsp_3.html#V2" target="_self">bounded</a>
 ;<br/>

<a NAME="E3:25"/><i><font color="Green">E12</font></i>: 
 <a href="bhsp_1.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font> is <a href="bhsp_3.html#V2" target="_self">bounded</a>
 
<b>by </b><i><a class="txt" href="bhsp_3.html#E2:25"><i><font color="Green">E11</font></i></a>, <a class="ref" href="bhsp_3.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E4:25"/>
<font color="Maroon">c<sub>2</sub></font> <a href="normsp_1.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="bhsp_1.html#K8">+</a> <span class="p1">(<span class="default"><a href="bhsp_1.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="bhsp_1.html#T71">BHSP_1:71</a></i>;<br/>
<b>hence </b><a NAME="E5:25"/>
<font color="Maroon">c<sub>2</sub></font> <a href="normsp_1.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> is <a href="bhsp_3.html#V2" target="_self">bounded</a>
 <b>by </b><i><a class="txt" href="bhsp_3.html#E1:25"><i><font color="Green">E10</font></i></a>, <a class="txt" href="bhsp_3.html#E3:25"><i><font color="Green">E12</font></i></a>, <a class="ref" href="bhsp_3.html#T18" target="_self">Th18</a></i>;<br/>


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