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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon" title="c2">seq</font> be   <a href="normsp_1.html#NM2" title="NORMSP_1:NM.2">sequence</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:61"/><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="bhsp_3.html#NR4" title="BHSP_3:NR.4">is_complete_space</a> 
 <b>and </b><br/><a NAME="E2:61"/><i><font color="Green" title="E25">A2</font></i>: 
<font color="Maroon" title="c2">seq</font> <a href="bhsp_3.html#NR1" title="BHSP_3:NR.1">is_Cauchy_sequence</a> 
 ;<br/>

<a NAME="E3:61"/>
<font color="Maroon" title="c2">seq</font> is <a href="bhsp_2.html#V1" title="BHSP_2:attr.1">convergent</a>
 
<b>by </b><i><a class="txt" href="bhsp_3.html#E1:61"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="bhsp_3.html#E2:61"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="bhsp_3.html#D6" target="_self" title="BHSP_3:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E4:61"/>
<font color="Maroon" title="c2">seq</font> is <a href="bhsp_3.html#V2" title="BHSP_3:attr.2">bounded</a>
 <b>by </b><i><a class="ref" href="bhsp_3.html#T24" target="_self" title="BHSP_3:th.24">Th24</a></i>;<br/>


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