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<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<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="E1:20"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">seq</font> <a href="ndiff_1.html#NR1" target="_self">is_not_0</a> 
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_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="E1:20_1"/>
<span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="lopban_3.html#K3">^\</a> <font color="Maroon">k</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="lopban_3.html#D6">LOPBAN_3:def 6</a></i>;<br/><b>hence </b><a NAME="E2:20_1"/>
<span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="lopban_3.html#K3">^\</a> <font color="Maroon">k</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">S</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20"/>
<font color="Maroon">seq</font> <a href="lopban_3.html#K3">^\</a> <font color="Maroon">k</font> <a href="ndiff_1.html#NR1" target="_self">is_not_0</a> 
 <b>by </b><i/>;<br/>


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