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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="clvect_1.html#NM5">ComplexNormSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nfcont_1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</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="E1:70"/><i><font color="Green">E64</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:70"/><b>then </b><i><font color="Green">E65</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1"><a href="ncfcont1.html#K2" target="_self">||.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="ncfcont1.html#K2" target="_self">.||</a></span>
 
<b>by </b><i><a class="ref" href="ncfcont1.html#D2" target="_self">Def2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><a NAME="E1:70_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="ncfcont1.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E2:70_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="ncfcont1.html#E1:70"><i><font color="Green">E64</font></i></a></i>;<br/><a NAME="E3:70_1"/><b>then </b><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1"><a href="ncfcont1.html#K2" target="_self">||.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="ncfcont1.html#K2" target="_self">.||</a></span>
 <b>by </b><i><a class="ref" href="ncfcont1.html#D2" target="_self">Def2</a></i>;<br/><b>thus </b><span class="p1"><a href="clvect_1.html#K10">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ncfcont1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="clvect_1.html#K10">.||</a></span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1"><a href="clvect_1.html#K5">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ncfcont1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="clvect_1.html#K5">.||</a></span>
<b>by </b><i><a class="ref" href="clvect_1.html#D16">CLVECT_1:def 16</a></i>
<br/>.= 
<span class="p1"><a href="clvect_1.html#K5">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span><a href="clvect_1.html#K5">.||</a></span>
<b>by </b><i><a class="txt" href="ncfcont1.html#E1:70"><i><font color="Green">E64</font></i></a>, <a class="ref" href="ncfcont1.html#T10" target="_self">Th10</a></i>
<br/>.= 
<span class="p1"><a href="ncfcont1.html#K2" target="_self">||.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="ncfcont1.html#K2" target="_self">.||</a></span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ncfcont1.html#E3:70_1"><i><font color="Green">E66</font></i></a>, <a class="ref" href="ncfcont1.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1"><a href="ncfcont1.html#K2" target="_self">||.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="ncfcont1.html#K2" target="_self">.||</a></span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ncfcont1.html#E3:70_1"><i><font color="Green">E66</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="ncfcont1.html#K2" target="_self">||.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="ncfcont1.html#K2" target="_self">.||</a></span> <a href="ncfcont1.html#K10" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="ncfcont1.html#E2:70"><i><font color="Green">E65</font></i></a>, <a class="ref" href="ncfcont1.html#T14" target="_self">Th14</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:70"/>
<span class="p1"><a href="clvect_1.html#K10">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ncfcont1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="clvect_1.html#K10">.||</a></span> <a href="funct_2.html#R2">=</a> <span class="p1"><a href="ncfcont1.html#K2" target="_self">||.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="ncfcont1.html#K2" target="_self">.||</a></span> <a href="ncfcont1.html#K10" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>

<b>thus </b> <a href="ncfcont1.html#K1" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ncfcont1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ncfcont1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ncfcont1.html#T2" target="_self">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="vfunct_2.html#K4">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ncfcont1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="ncfcont1.html#E1:70"><i><font color="Green">E64</font></i></a>, <a class="ref" href="ncfcont1.html#T47" target="_self">Th47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="vfunct_2.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ncfcont1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="vfunct_2.html#T23">VFUNCT_2:23</a></i>
;<br/>


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