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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">g</font>, <font color="Maroon" title="c3">x</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c4">seq</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:38"/><i><font color="Green" title="E28">A1</font></i>: 
<font color="Maroon" title="c4">seq</font> is <a href="bhsp_2.html#V1" title="BHSP_2:attr.1">convergent</a>
 <b>and </b><br/><a NAME="E2:38"/><i><font color="Green" title="E29">A2</font></i>: 
 <a href="bhsp_2.html#K1" title="BHSP_2:func.1">lim</a> <font color="Maroon" title="c4">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font>
 ;<br/>

<a NAME="E3:38"/><i><font color="Green" title="E30">A3</font></i>: 
<font color="Maroon" title="c4">seq</font> <a href="bhsp_1.html#K7" title="BHSP_1:func.7">+</a> <font color="Maroon" title="c3">x</font> is <a href="bhsp_2.html#V1" title="BHSP_2:attr.1">convergent</a>
 
<b>by </b><i><a class="txt" href="bhsp_2.html#E1:38"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="bhsp_2.html#T7" target="_self" title="BHSP_2:th.7">Th7</a></i>;<br/>
<a NAME="E4:38"/>
 <a href="bhsp_2.html#K1" title="BHSP_2:func.1">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq</font> <a href="bhsp_1.html#K7" title="BHSP_1:func.7">+</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">x</font>
 
<b>by </b><i><a class="txt" href="bhsp_2.html#E1:38"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="bhsp_2.html#E2:38"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="bhsp_2.html#T17" target="_self" title="BHSP_2:th.17">Th17</a></i>;<br/>
<b>hence </b><a NAME="E5:38"/>
( <span class="p1"><a href="bhsp_2.html#K2" title="BHSP_2:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">seq</font> <a href="bhsp_1.html#K7" title="BHSP_1:func.7">+</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="normsp_1.html#K5" title="NORMSP_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span><a href="bhsp_2.html#K2" title="BHSP_2:func.2">.||</a></span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1"><a href="bhsp_2.html#K2" title="BHSP_2:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">seq</font> <a href="bhsp_1.html#K7" title="BHSP_1:func.7">+</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="normsp_1.html#K5" title="NORMSP_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span></span><a href="bhsp_2.html#K2" title="BHSP_2:func.2">.||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="txt" href="bhsp_2.html#E3:38"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="bhsp_2.html#T22" target="_self" title="BHSP_2:th.22">Th22</a></i>;<br/>


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