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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="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</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="E1:42"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="bhsp_2.html#V1" target="_self">convergent</a>
 <b>and </b><br/><a NAME="E2:42"/><i><font color="Green">E29</font></i>: 
 <a href="bhsp_2.html#K1" target="_self">lim</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E3:42"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is <a href="bhsp_2.html#V1" target="_self">convergent</a>
 <b>and </b><br/><a NAME="E4:42"/><i><font color="Green">E31</font></i>: 
 <a href="bhsp_2.html#K1" target="_self">lim</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E5:42"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="normsp_1.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> is <a href="bhsp_2.html#V1" target="_self">convergent</a>
 
<b>by </b><i><a class="txt" href="bhsp_2.html#E1:42"><i><font color="Green">E28</font></i></a>, <a class="txt" href="bhsp_2.html#E3:42"><i><font color="Green">E30</font></i></a>, <a class="ref" href="bhsp_2.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E6:42"/>
 <a href="bhsp_2.html#K1" target="_self">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="normsp_1.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="bhsp_2.html#E1:42"><i><font color="Green">E28</font></i></a>, <a class="txt" href="bhsp_2.html#E2:42"><i><font color="Green">E29</font></i></a>, <a class="txt" href="bhsp_2.html#E3:42"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bhsp_2.html#E4:42"><i><font color="Green">E31</font></i></a>, <a class="ref" href="bhsp_2.html#T14" target="_self">Th14</a></i>;<br/>
<b>hence </b><a NAME="E7:42"/>
(  <a href="bhsp_2.html#K3" target="_self">dist</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="normsp_1.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><a href="bhsp_2.html#K3" target="_self">dist</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="normsp_1.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="txt" href="bhsp_2.html#E5:42"><i><font color="Green">E32</font></i></a>, <a class="ref" href="bhsp_2.html#T24" target="_self">Th24</a></i>;<br/>


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