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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="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><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><a NAME="E1:10"/>
<font color="Maroon">c<sub>3</sub></font> <a href="bhsp_3.html#NR1" target="_self">is_Cauchy_sequence</a> 
 ;<br/>

<a NAME="E2:10"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="bhsp_1.html#K7">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="bhsp_3.html#NR1" target="_self">is_Cauchy_sequence</a> 
 
<b>by </b><i><a class="ref" href="bhsp_3.html#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E3:10"/>
<font color="Maroon">c<sub>3</sub></font> <a href="normsp_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="bhsp_3.html#NR1" target="_self">is_Cauchy_sequence</a> 
 <b>by </b><i><a class="ref" href="bhsp_1.html#T78">BHSP_1:78</a></i>;<br/>


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