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<b>let </b><font color="Maroon" title="c1">k</font>, <font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">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" title="E8">A1</font></i>: 
 <a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">PSeg</a> <font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">PSeg</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">PSeg</a> <font color="Maroon" title="c2">n</font></span>)</span>
 ;<br/><b>assume </b><a NAME="E2:9_1"/>
not <font color="Maroon" title="c1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font>
 ;<br/><a NAME="E3:9_1"/><b>then </b>
 <a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">PSeg</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">PSeg</a> <font color="Maroon" title="c1">k</font>
 <b>by </b><i><a class="txt" href="algseq_1.html#E1:9_1"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="algseq_1.html#T15" target="_self" title="ALGSEQ_1:th.15">Th15</a></i>;<br/><b>hence </b><a NAME="E4:9_1"/>
<font color="Maroon" title="c1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font>
 <b>by </b><i><a class="ref" href="algseq_1.html#T14" target="_self" title="ALGSEQ_1:th.14">Th14</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:9"/>
( (  <a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">PSeg</a> <font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">PSeg</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">PSeg</a> <font color="Maroon" title="c2">n</font></span>)</span> or  <a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">PSeg</a> <font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">PSeg</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K2" title="ALGSEQ_1:func.2">PSeg</a> <font color="Maroon" title="c1">k</font></span>)</span> ) implies <font color="Maroon" title="c1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font> )
 ;<br/>


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