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<b>let </b><font color="Maroon">S</font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">T</font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">h</font> be   <a href="nfcont_1.html#NM1">PartFunc</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">seq</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">S</font>;<br/>







<b>assume </b><a NAME="E1:32"/><i><font color="Green">E43</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">h</font>
 ;<br/>

<a NAME="E2:32"/><b>then </b><i><font color="Green">E44</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"><a href="nfcont_1.html#K2" target="_self">||.</a><span class="default"><font color="Maroon">h</font></span><a href="nfcont_1.html#K2" target="_self">.||</a></span>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_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="E1:32_1"/>
<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#K5">rng</a> <font color="Maroon">seq</font>
 <b>by </b><i/>;<br/><a NAME="E2:32_1"/><b>then </b>
<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> <font color="Maroon">h</font>
 <b>by </b><i/>;<br/><a NAME="E3:32_1"/><b>then </b><i><font color="Green">E55</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"><a href="nfcont_1.html#K2" target="_self">||.</a><span class="default"><font color="Maroon">h</font></span><a href="nfcont_1.html#K2" target="_self">.||</a></span>
 <b>by </b><i/>;<br/><b>thus </b><span class="p1"><a href="normsp_1.html#K7">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="nfcont_1.html#K3" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span><a href="normsp_1.html#K7">.||</a></span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> = 
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="nfcont_1.html#K3" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span>
<b>by </b><i><a class="ref" href="normsp_1.html#D10">NORMSP_1:def 10</a></i>
<br/>.= 
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span></span>)</span></span><a href="normsp_1.html#K1">.||</a></span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1"><a href="nfcont_1.html#K2" target="_self">||.</a><span class="default"><font color="Maroon">h</font></span><a href="nfcont_1.html#K2" target="_self">.||</a></span> <a href="seq_1.html#K2">.</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>, </i>
<br/>.= 
<span class="p1"><a href="nfcont_1.html#K2" target="_self">||.</a><span class="default"><font color="Maroon">h</font></span><a href="nfcont_1.html#K2" target="_self">.||</a></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="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="nfcont_1.html#K2" target="_self">||.</a><span class="default"><font color="Maroon">h</font></span><a href="nfcont_1.html#K2" target="_self">.||</a></span> <a href="nfcont_1.html#K4" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font>
<b>by </b><i>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:32"/>
<span class="p1"><a href="normsp_1.html#K7">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="nfcont_1.html#K3" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span><a href="normsp_1.html#K7">.||</a></span> <a href="funct_2.html#R2">=</a> <span class="p1"><a href="nfcont_1.html#K2" target="_self">||.</a><span class="default"><font color="Maroon">h</font></span><a href="nfcont_1.html#K2" target="_self">.||</a></span> <a href="nfcont_1.html#K4" target="_self">*</a> <font color="Maroon">seq</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>

<b>thus </b> <a href="nfcont_1.html#K1" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="nfcont_1.html#K3" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="normsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="nfcont_1.html#K3" target="_self">*</a> <font color="Maroon">seq</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="vfunct_1.html#K4">(#)</a> <font color="Maroon">h</font></span>)</span> <a href="nfcont_1.html#K3" target="_self">*</a> <font color="Maroon">seq</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="vfunct_1.html#K6">-</a> <font color="Maroon">h</font></span>)</span> <a href="nfcont_1.html#K3" target="_self">*</a> <font color="Maroon">seq</font>
<b>by </b><i><a class="ref" href="vfunct_1.html#T29">VFUNCT_1:29</a></i>
;<br/>


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