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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">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>assume </b><a NAME="E1:21"/><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> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 ;<br/>

<a NAME="E2:21"/><b>then </b>
<font color="Maroon">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>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/>
<a NAME="E3:21"/><b>then </b>
not <font color="Maroon">k</font> <a href="algseq_1.html#R1" target="_self">is_at_least_length_of</a> <font color="Maroon">p</font>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:21"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> )
 <b>by </b><i/>;<br/>
<a NAME="E6:21"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E7:21"/><b>then </b>
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>hence </b><a NAME="E8:21"/>
<font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>


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