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<b>let </b><font color="Maroon">R</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">p</font> be   <a href="algseq_1.html#NM1">AlgSequence</a> of <font color="Maroon">R</font>;<br/>



<b>thus </b><a NAME="E1:28"/>
( <font color="Maroon">p</font> <a href="funct_2.html#R2">=</a> <span class="p1"><a href="algseq_1.html#K5" target="_self">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span></span><a href="algseq_1.html#K5" target="_self">%&gt;</a></span> implies  <a href="algseq_1.html#K3" target="_self">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E2:28"/>
(  <a href="algseq_1.html#K3" target="_self">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 0 implies <font color="Maroon">p</font> <a href="funct_2.html#R2">=</a> <span class="p1"><a href="algseq_1.html#K5" target="_self">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span></span><a href="algseq_1.html#K5" target="_self">%&gt;</a></span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:28_1"/><i><font color="Green">E26</font></i>: 
 <a href="algseq_1.html#K3" target="_self">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:28_1"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="algseq_1.html#K3" target="_self">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="algseq_1.html#K3" target="_self">len</a> <span class="p1"><a href="algseq_1.html#K5" target="_self">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span></span><a href="algseq_1.html#K5" target="_self">%&gt;</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E3:28_1"/>
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="algseq_1.html#K3" target="_self">len</a> <font color="Maroon">p</font> holds <br/><font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="algseq_1.html#K5" target="_self">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span></span><a href="algseq_1.html#K5" target="_self">%&gt;</a></span> <a href="funct_2.html#K3">.</a> <font color="Olive">k</font>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/>
<b>hence </b><a NAME="E4:28_1"/>
<font color="Maroon">p</font> <a href="funct_2.html#R2">=</a> <span class="p1"><a href="algseq_1.html#K5" target="_self">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span></span><a href="algseq_1.html#K5" target="_self">%&gt;</a></span>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>


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