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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">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1"/><i><font color="Green">E26</font></i>: 
 <a href="algseq_1.html#K2" target="_self">PSeg</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2" target="_self">PSeg</a> <font color="Maroon">k</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2" target="_self">PSeg</a> <font color="Maroon">n</font></span>)</span>
 ;<br/><b>assume </b><a NAME="E2:9_1"/>
not <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 ;<br/><a NAME="E3:9_1"/><b>then </b>
 <a href="algseq_1.html#K2" target="_self">PSeg</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="algseq_1.html#K2" target="_self">PSeg</a> <font color="Maroon">k</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:9_1"/>
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:9"/>
( (  <a href="algseq_1.html#K2" target="_self">PSeg</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2" target="_self">PSeg</a> <font color="Maroon">k</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2" target="_self">PSeg</a> <font color="Maroon">n</font></span>)</span> or  <a href="algseq_1.html#K2" target="_self">PSeg</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2" target="_self">PSeg</a> <font color="Maroon">n</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2" target="_self">PSeg</a> <font color="Maroon">k</font></span>)</span> ) implies <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> )
 ;<br/>


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