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<b>let </b><font color="Maroon">CNS</font> be   <a href="clvect_1.html#NM5">ComplexNormSpace</a>;<br/><b>let </b><font color="Maroon">RNS</font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">h1</font> be   <a href="nfcont_1.html#NM1">PartFunc</a> of <font color="Maroon">RNS</font>,<font color="Maroon">CNS</font>, <font color="Maroon">h2</font> be   <a href="nfcont_1.html#NM1">PartFunc</a> of <font color="Maroon">RNS</font>,<font color="Maroon">CNS</font>;<br/><b>let </b><font color="Maroon">seq</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">RNS</font>;<br/>







<b>assume </b><a NAME="E1:66"/><i><font color="Green">E34</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">h1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">h2</font></span>)</span>
 ;<br/>

<a NAME="E2:66"/>
( <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">h1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">h2</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h1</font> &amp; <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">h1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">h2</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h2</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E3:66"/><b>then </b><i><font color="Green">E35</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h1</font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h2</font> )
 
<b>by </b><i><a class="ref" href="ncfcont1.html#D10" target="_self">Def10</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:66"/><i><font color="Green">E54</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="vfunct_2.html#K1">+</a> <font color="Maroon">h2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ncfcont1.html#D10" target="_self">Def10</a>, <a class="ref" href="vfunct_2.html#D1">VFUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:66"/><i><font color="Green">E56</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="vfunct_2.html#K2">-</a> <font color="Maroon">h2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ncfcont1.html#D10" target="_self">Def10</a>, <a class="ref" href="vfunct_2.html#D2">VFUNCT_2:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E1:66_1"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="vfunct_2.html#K1">+</a> <font color="Maroon">h2</font></span>)</span>
 <b>by </b><i><a class="ref" href="ncfcont1.html#D12" target="_self">Def12</a>, </i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h1</font> <a href="vfunct_2.html#K1">+</a> <font color="Maroon">h2</font></span>)</span> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="vfunct_2.html#K1">+</a> <font color="Maroon">h2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="ncfcont1.html#D12" target="_self">Def12</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">h2</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ncfcont1.html#D14" target="_self">Def14</a>, <a class="ref" href="vfunct_2.html#D1">VFUNCT_2:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h1</font> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">h2</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ncfcont1.html#D11" target="_self">Def11</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h1</font> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h2</font> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="ncfcont1.html#D11" target="_self">Def11</a>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:66"/>
<span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="vfunct_2.html#K1">+</a> <font color="Maroon">h2</font></span>)</span> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="clvect_1.html#K6">+</a> <span class="p1">(<span class="default"><font color="Maroon">h2</font> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span>
 <b>by </b><i><a class="ref" href="clvect_1.html#D11">CLVECT_1:def 11</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E1:66_2"/><i><font color="Green">E110</font></i>: 
<font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="vfunct_2.html#K2">-</a> <font color="Maroon">h2</font></span>)</span>
 <b>by </b><i><a class="ref" href="ncfcont1.html#D13" target="_self">Def13</a>, </i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h1</font> <a href="vfunct_2.html#K2">-</a> <font color="Maroon">h2</font></span>)</span> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="vfunct_2.html#K2">-</a> <font color="Maroon">h2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="ncfcont1.html#D13" target="_self">Def13</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">h2</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ncfcont1.html#D14" target="_self">Def14</a>, <a class="ref" href="vfunct_2.html#D2">VFUNCT_2:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h1</font> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">h2</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ncfcont1.html#D11" target="_self">Def11</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h1</font> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h2</font> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="ncfcont1.html#D11" target="_self">Def11</a>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:66"/>
<span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="vfunct_2.html#K2">-</a> <font color="Maroon">h2</font></span>)</span> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="clvect_1.html#K7">-</a> <span class="p1">(<span class="default"><font color="Maroon">h2</font> <a href="ncfcont1.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span>
 <b>by </b><i><a class="ref" href="clvect_1.html#D12">CLVECT_1:def 12</a></i>;<br/>


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