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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> 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="E1:61"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="bhsp_3.html#NR4" target="_self">is_complete_space</a> 
 <b>and </b><br/><a NAME="E2:61"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="bhsp_3.html#NR1" target="_self">is_Cauchy_sequence</a> 
 ;<br/>

<a NAME="E3:61"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="bhsp_2.html#V1">convergent</a>
 
<b>by </b><i><a class="txt" href="bhsp_3.html#E1:61"><i><font color="Green">E24</font></i></a>, <a class="txt" href="bhsp_3.html#E2:61"><i><font color="Green">E25</font></i></a>, <a class="ref" href="bhsp_3.html#D6" target="_self">Def6</a></i>;<br/>
<b>hence </b><a NAME="E4:61"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="bhsp_3.html#V2" target="_self">bounded</a>
 <b>by </b><i><a class="ref" href="bhsp_3.html#T24" target="_self">Th24</a></i>;<br/>


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