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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L2">ZeroStr</a> ;<br/><b>let </b><font color="Maroon">z0</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:41"/>
<font color="Maroon">z0</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 ;<br/>

<a NAME="E2:41"/><b>then </b>
<span class="p1"><a href="algseq_1.html#K5">&lt;%</a><span class="default"><font color="Maroon">z0</font></span><a href="algseq_1.html#K5">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="algseq_1.html#D6">ALGSEQ_1:def 6</a></i>;<br/>
<a NAME="E3:41"/><b>then </b>
<span class="p1"><a href="algseq_1.html#K5">&lt;%</a><span class="default"><font color="Maroon">z0</font></span><a href="algseq_1.html#K5">%&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="algseq_1.html#K5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span></span><a href="algseq_1.html#K5">%&gt;</a></span>
 
<b>by </b><i><a class="ref" href="algseq_1.html#D6">ALGSEQ_1:def 6</a></i>;<br/>
<a NAME="E4:41"/><b>then </b>
 <a href="algseq_1.html#K3">len</a> <span class="p1"><a href="algseq_1.html#K5">&lt;%</a><span class="default"><font color="Maroon">z0</font></span><a href="algseq_1.html#K5">%&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="algseq_1.html#T31">ALGSEQ_1:31</a></i>;<br/>
<a NAME="E5:41"/><b>then </b>
 <a href="algseq_1.html#K3">len</a> <span class="p1"><a href="algseq_1.html#K5">&lt;%</a><span class="default"><font color="Maroon">z0</font></span><a href="algseq_1.html#K5">%&gt;</a></span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
;<br/>
<a NAME="E6:41"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="algseq_1.html#K3">len</a> <span class="p1"><a href="algseq_1.html#K5">&lt;%</a><span class="default"><font color="Maroon">z0</font></span><a href="algseq_1.html#K5">%&gt;</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>assume </b><a NAME="E7:41"/>
 <a href="algseq_1.html#K3">len</a> <span class="p1"><a href="algseq_1.html#K5">&lt;%</a><span class="default"><font color="Maroon">z0</font></span><a href="algseq_1.html#K5">%&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/>

<a NAME="E8:41"/><b>then </b>
 <a href="algseq_1.html#K3">len</a> <span class="p1"><a href="algseq_1.html#K5">&lt;%</a><span class="default"><font color="Maroon">z0</font></span><a href="algseq_1.html#K5">%&gt;</a></span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E9:41"/>
contradiction
 <b>by </b><i><a class="ref" href="algseq_1.html#D6">ALGSEQ_1:def 6</a></i>;<br/>


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