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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><a NAME="E1:18"/>
<font color="Maroon" title="c2">seq</font> is <a href="bhsp_2.html#V1" title="BHSP_2:attr.1">convergent</a>
 ;<br/>

<a NAME="E2:18"/><b>then </b>
 <a href="bhsp_2.html#K1" title="BHSP_2:func.1">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="normsp_1.html#K6" title="NORMSP_1:func.6">*</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><a href="bhsp_2.html#K1" title="BHSP_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font></span>)</span>
 
<b>by </b><i><a class="ref" href="bhsp_2.html#T15" target="_self" title="BHSP_2:th.15">Th15</a></i>;<br/>
<a NAME="E3:18"/><b>then </b>
 <a href="bhsp_2.html#K1" title="BHSP_2:func.1">lim</a> <span class="p1">(<span class="default"><a href="bhsp_1.html#K6" title="BHSP_1:func.6">-</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><a href="bhsp_2.html#K1" title="BHSP_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font></span>)</span>
 
<b>by </b><i><a class="ref" href="bhsp_1.html#T77" title="BHSP_1:th.77">BHSP_1:77</a></i>;<br/>
<b>hence </b><a NAME="E4:18"/>
 <a href="bhsp_2.html#K1" title="BHSP_2:func.1">lim</a> <span class="p1">(<span class="default"><a href="bhsp_1.html#K6" title="BHSP_1:func.6">-</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><a href="bhsp_2.html#K1" title="BHSP_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font></span>)</span>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T29" title="RLVECT_1:th.29">RLVECT_1:29</a></i>;<br/>


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