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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="csspace.html#NM1">ComplexUnitarySpace</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> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:39"/>
( <font color="Maroon">c<sub>4</sub></font> is <a href="clvect_2.html#V1" target="_self">convergent</a> &amp;  <a href="clvect_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> )
 ;<br/>

<a NAME="E2:39"/><b>then </b>
( <span class="p1"><a href="clvect_2.html#K2" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="csspace.html#K17">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span><a href="clvect_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="clvect_2.html#K2" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="csspace.html#K17">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span><a href="clvect_2.html#K2" target="_self">.||</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="csspace.html#K13">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span><a href="csspace.html#K13">.||</a></span> )
 
<b>by </b><i><a class="txt" href="clvect_2.html#E37"><i><font color="Green">Lemma26</font></i></a></i>;<br/>
<a NAME="E3:39"/><b>then </b>
( <span class="p1"><a href="clvect_2.html#K2" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="clvect_1.html#K8">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="clvect_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="clvect_2.html#K2" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="clvect_1.html#K8">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="clvect_2.html#K2" target="_self">.||</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="csspace.html#K13">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span><a href="csspace.html#K13">.||</a></span> )
 
<b>by </b><i><a class="ref" href="csspace.html#T78">CSSPACE:78</a></i>;<br/>
<b>hence </b><a NAME="E4:39"/>
( <span class="p1"><a href="clvect_2.html#K2" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="clvect_1.html#K8">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="clvect_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="clvect_2.html#K2" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="clvect_1.html#K8">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="clvect_2.html#K2" target="_self">.||</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="csspace.html#K13">||.</a><span class="default"><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><a href="csspace.html#K13">.||</a></span> )
 <b>by </b><i><a class="ref" href="rlvect_1.html#D11">RLVECT_1:def 11</a></i>;<br/>


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