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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><b>that </b><br/><a NAME="E1:36"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="bhsp_2.html#V1" target="_self">convergent</a>
 <b>and </b><br/><a NAME="E2:36"/><i><font color="Green">E27</font></i>: 
 <a href="bhsp_2.html#K1" target="_self">lim</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:36"/><i><font color="Green">E28</font></i>: 
 <a href="bhsp_1.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font> is <a href="bhsp_2.html#V1" target="_self">convergent</a>
 
<b>by </b><i><a class="txt" href="bhsp_2.html#E1:36"><i><font color="Green">E26</font></i></a>, <a class="ref" href="bhsp_2.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E4:36"/>
 <a href="bhsp_2.html#K1" target="_self">lim</a> <span class="p1">(<span class="default"><a href="bhsp_1.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="bhsp_2.html#E1:36"><i><font color="Green">E26</font></i></a>, <a class="txt" href="bhsp_2.html#E2:36"><i><font color="Green">E27</font></i></a>, <a class="ref" href="bhsp_2.html#T16" target="_self">Th16</a></i>;<br/>
<b>hence </b><a NAME="E5:36"/>
( <span class="p1"><a href="bhsp_2.html#K2" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bhsp_1.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="normsp_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="bhsp_2.html#K2" target="_self">.||</a></span> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1"><a href="bhsp_2.html#K2" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bhsp_1.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="normsp_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="bhsp_2.html#K2" target="_self">.||</a></span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="txt" href="bhsp_2.html#E3:36"><i><font color="Green">E28</font></i></a>, <a class="ref" href="bhsp_2.html#T22" target="_self">Th22</a></i>;<br/>


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