<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">CNS</font> be   <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">RNS</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">h</font> be   <a href="nfcont_1.html#NM1" title="NFCONT_1:NM.1">PartFunc</a> of <font color="Maroon" title="c2">RNS</font>,<font color="Maroon" title="c1">CNS</font>;<br/><b>let </b><font color="Maroon" title="c4">seq</font> be   <a href="normsp_1.html#NM2" title="NORMSP_1:NM.2">sequence</a> of <font color="Maroon" title="c2">RNS</font>;<br/>







<b>assume </b><a NAME="E1:72"/><i><font color="Green" title="E66">A1</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">seq</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font>
 ;<br/>

<a NAME="E2:72"/><b>then </b><i><font color="Green" title="E67">A2</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">seq</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="ncfcont1.html#K4" title="NCFCONT1:func.4">||.</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="ncfcont1.html#K4" title="NCFCONT1:func.4">.||</a></span>
 
<b>by </b><i><a class="ref" href="ncfcont1.html#D4" target="_self" title="NCFCONT1:def.4">Def4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><a NAME="E1:72_1"/>
<font color="Maroon" title="c4">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">seq</font>
 <b>by </b><i><a class="ref" href="nfcont_1.html#T6" title="NFCONT_1:th.6">NFCONT_1:6</a></i>;<br/><a NAME="E2:72_1"/><b>then </b>
<font color="Maroon" title="c4">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font>
 <b>by </b><i><a class="txt" href="ncfcont1.html#E1:72"><i><font color="Green" title="E66">A1</font></i></a></i>;<br/><a NAME="E3:72_1"/><b>then </b><i><font color="Green" title="E68">A3</font></i>: 
<font color="Maroon" title="c4">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="ncfcont1.html#K4" title="NCFCONT1:func.4">||.</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="ncfcont1.html#K4" title="NCFCONT1:func.4">.||</a></span>
 <b>by </b><i><a class="ref" href="ncfcont1.html#D4" target="_self" title="NCFCONT1:def.4">Def4</a></i>;<br/><b>thus </b><span class="p1"><a href="clvect_1.html#K10" title="CLVECT_1:func.10">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="ncfcont1.html#K7" title="NCFCONT1:func.7">*</a> <font color="Maroon" title="c4">seq</font></span>)</span></span><a href="clvect_1.html#K10" title="CLVECT_1:func.10">.||</a></span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">n</font> = 
<span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="ncfcont1.html#K7" title="NCFCONT1:func.7">*</a> <font color="Maroon" title="c4">seq</font></span>)</span> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span>
<b>by </b><i><a class="ref" href="clvect_1.html#D16" title="CLVECT_1:def.16">CLVECT_1:def 16</a></i>
<br/>.= 
<span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span>
<b>by </b><i><a class="txt" href="ncfcont1.html#E1:72"><i><font color="Green" title="E66">A1</font></i></a>, <a class="ref" href="ncfcont1.html#T12" target="_self" title="NCFCONT1:th.12">Th12</a></i>
<br/>.= 
<span class="p1"><a href="ncfcont1.html#K4" title="NCFCONT1:func.4">||.</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="ncfcont1.html#K4" title="NCFCONT1:func.4">.||</a></span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font></span>)</span>
<b>by </b><i><a class="txt" href="ncfcont1.html#E3:72_1"><i><font color="Green" title="E68">A3</font></i></a>, <a class="ref" href="ncfcont1.html#D4" target="_self" title="NCFCONT1:def.4">Def4</a></i>
<br/>.= 
<span class="p1"><a href="ncfcont1.html#K4" title="NCFCONT1:func.4">||.</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="ncfcont1.html#K4" title="NCFCONT1:func.4">.||</a></span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font></span>)</span>
<b>by </b><i><a class="txt" href="ncfcont1.html#E3:72_1"><i><font color="Green" title="E68">A3</font></i></a>, <a class="ref" href="finseq_4.html#D4" title="FINSEQ_4:def.4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="ncfcont1.html#K4" title="NCFCONT1:func.4">||.</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="ncfcont1.html#K4" title="NCFCONT1:func.4">.||</a></span> <a href="nfcont_1.html#K4" title="NFCONT_1:func.4">*</a> <font color="Maroon" title="c4">seq</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">n</font>
<b>by </b><i><a class="txt" href="ncfcont1.html#E2:72"><i><font color="Green" title="E67">A2</font></i></a>, <a class="ref" href="nfcont_1.html#T9" title="NFCONT_1:th.9">NFCONT_1:9</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:72"/>
<span class="p1"><a href="clvect_1.html#K10" title="CLVECT_1:func.10">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="ncfcont1.html#K7" title="NCFCONT1:func.7">*</a> <font color="Maroon" title="c4">seq</font></span>)</span></span><a href="clvect_1.html#K10" title="CLVECT_1:func.10">.||</a></span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1"><a href="ncfcont1.html#K4" title="NCFCONT1:func.4">||.</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="ncfcont1.html#K4" title="NCFCONT1:func.4">.||</a></span> <a href="nfcont_1.html#K4" title="NFCONT_1:func.4">*</a> <font color="Maroon" title="c4">seq</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>

<b>thus </b> <a href="ncfcont1.html#K1" title="NCFCONT1:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="ncfcont1.html#K7" title="NCFCONT1:func.7">*</a> <font color="Maroon" title="c4">seq</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="clvect_1.html#K9" title="CLVECT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="ncfcont1.html#K7" title="NCFCONT1:func.7">*</a> <font color="Maroon" title="c4">seq</font></span>)</span>
<b>by </b><i><a class="ref" href="ncfcont1.html#T2" target="_self" title="NCFCONT1:th.2">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="vfunct_2.html#K4" title="VFUNCT_2:func.4">(#)</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="ncfcont1.html#K7" title="NCFCONT1:func.7">*</a> <font color="Maroon" title="c4">seq</font>
<b>by </b><i><a class="txt" href="ncfcont1.html#E1:72"><i><font color="Green" title="E66">A1</font></i></a>, <a class="ref" href="ncfcont1.html#T49" target="_self" title="NCFCONT1:th.49">Th49</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="vfunct_2.html#K6" title="VFUNCT_2:func.6">-</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="ncfcont1.html#K7" title="NCFCONT1:func.7">*</a> <font color="Maroon" title="c4">seq</font>
<b>by </b><i><a class="ref" href="vfunct_2.html#T23" title="VFUNCT_2:th.23">VFUNCT_2:23</a></i>
;<br/>


</div>
